2020-10-22T13:34:55Zhttp://edoc.mpg.de/ac_ft_oai.ploai:edoc.mpg.de:26982009-03-316:84
Formation of the universe : From classical to quantum cosmology
Nicolai, Hermann
Pössel, Markus
We give a brief overview of the role of quantum theory in cosmology, reviewing the standard model of classical cosmology, inflation and quantum cosmology. Plenary Talk given by H. Nicolai on December 13, 2000 at the Quantum Theory Centenary ''''100 Jahre Quantentheorie, Berlin
2001
Article
http://edoc.mpg.de/2698
urn:ISSN:1521-3889
info:doi/10.1002/1521-3889(200102)10:1/2<123::AID-ANDP123>3.0.CO;2-B
Annalen der Physik, v.10, 123-130 (2001)
en
oai:edoc.mpg.de:27012009-03-316:84
Microlocal spectrum condition and Hadamard form for vector-valued quantum fields in curved spacetime
Sahlmann, Hanno
Verch, Rainer
The characterization of Hadamard states in terms of a specific form of the wavefront set of their two-point functions has been developed some years ago by Radzikowski for scalar fields on a four-dimensional globally hyperbolic spacetime, and initiated a major progress in the understanding of Hadamard states and the further development of quantum field theory in curved spacetime. In the present work, the characterization of Hadamard states through a particular form of the wavefront set of their two-point functions will be generalized from scalar fields to vector fields (sections in a vector bundle) which are subject to a wave-equation and are quantized so as to fulfill the covariant canonical commutation relations, or which obey a Dirac equation and are quantized according to the covariant anti-commutation relations, in any globally hyperbolic spacetime having dimension three or higher. In proving this result, a gap which is present in the published proof for the scalar field case will be removed. Moreover we determine the short-distance scaling limits of Hadamard states for vector-bundle valued fields, finding them to coincide with the corresponding flat-space, massless vacuum states.
2001
Article
http://edoc.mpg.de/2701
Reviews in Mathematical Physics, v.13, 1203-1246 (2001)
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oai:edoc.mpg.de:27032009-03-316:84
On non-commutative N=2 Super Yang Mills
Armoni, Adi
Minasian, Ruben
Theisen, Stefan
We discuss the Seiberg-Witten solution of the non-commutative N=2 U(N) SYM model. The solution is described in terms of the ordinary Seiberg-Witten curve of the SU(N) theory plus an additional free U(1). Hence, at the two-derivative approximation the theory flows to the ordinary commutative theory in the infra-red (k<1/sqrt(theta)). In particular, the center U(1) is free and it decouples from the other U(1)s. In addition, no UV/IR mixing is found.
2001
Article
http://edoc.mpg.de/2703
urn:ISSN:0370-2693
info:doi/10.1016/S0370-2693(01)00763-8
Physics Letters B, v.513, 406-412 (2001)
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oai:edoc.mpg.de:27042009-03-316:84
Coherent States for Canonical Quantum General Relativity and the Infinite Tensor Product Extension
Sahlmann, Hanno
Thiemann, Thomas
Winkler, Oliver
We summarize a recently proposed concrete programme for investigating the (semi)classical limit of canonical, Lorentzian, continuum quantum general relativity in four spacetime dimensions. The analysis is based on a novel set of coherent states labelled by graphs. These fit neatly together with an Infinite Tensor Product (ITP) extension of the currently used Hilbert space. The ITP construction enables us to give rigorous meaning to the infinite volume (thermodynamic) limit of the theory which has been out of reach so far.
2001
Article
http://edoc.mpg.de/2704
Nuclear Physics B, v.606, 401-440 (2001)
en
oai:edoc.mpg.de:27052009-03-316:84
R^4 couplings, the fundamental membrane and exceptional theta correspondences
Pioline, Boris
Nicolai, Hermann
Plefka, Jan
Waldron, Andrew
This letter is an attempt to carry out a first-principle computation in M-theory using the point of view that the eleven-dimensional membrane gives the fundamental degrees of freedom of M-theory. Our aim is to derive the exact BPS $R^4$ couplings in toroidal compactifications of M-theory from the toroidal BPS membrane, by pursuing the analogy with the one-loop string theory computation. We exhibit an $Sl(3,Zint)$ modular invariance hidden in the light-cone gauge (but obvious in the Polyakov approach), and recover the correct classical spectrum and membrane instantons; the summation measure however is off. We argue that the correct membrane amplitude should be given by an exceptional theta correspondence lifting $Sl(3,Zint)$ modular forms to $exc(Zint)$ automorphic forms, generalizing the usual theta lift between $Sl(2,Zint)$ and $SO(d,d,Zint)$ in string theory, and outline the construction of such objects. The exceptional correspondence $Sl(3)imes E_6subset E_8$ offers the interesting prospect of solving the membrane small volume divergence and unifying membranes with five-branes.
2001
Article
http://edoc.mpg.de/2705
urn:ISSN:1126-6708
info:doi/10.1088/1126-6708/2001/03/036
Journal of High Energy Physics, v.03 (2001)
en
oai:edoc.mpg.de:27142009-03-316:84
Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions
Nicolai, Hermann
Samtleben, Henning
We present the maximally supersymmetric three-dimensional gauged supergravities. Owing to the special properties of three dimensions -- especially the on-shell duality between vector and scalar fields, and the purely topological character of (super)gravity -- they exhibit an even richer structure than the gauged supergravities in higher dimensions. The allowed gauge groups are subgroups of the global E_8 symmetry of ungauged N=16 supergravity. They include the regular series SO(p,8-p) x SO(p,8-p) for all p=0,1,...,4, the group E_8 itself, as well as various noncompact forms of the exceptional groups E_7, E_6 and F_4 x G_2. We show that all these theories admit maximally supersymmetric ground states, and determine their background isometries, which are superextensions of the anti-de Sitter group SO(2,2). The very existence of these theories is argued to point to a new supergravity beyond the standard D=11 supergravity.
2001
Article
http://edoc.mpg.de/2714
urn:ISSN:1126-6708
info:doi/10.1088/1126-6708/2001/04/022
Journal of High Energy Physics, v.04 (2001)
en
oai:edoc.mpg.de:27152009-03-316:84
Jet coordinates for local BRST cohomology
Brandt, Friedemann
The construction of appropriate jet space coordinates for calculating local BRST cohomology groups is discussed. The relation to tensor calculus is briefly reviewed too.
2001
Article
http://edoc.mpg.de/2715
Letters in Mathematical Physics, v.55, 149-159 (2001)
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oai:edoc.mpg.de:27162009-03-316:84
A proper-time cure for the conformal sickness in quantum gravity
Dasgupta, Arundhati
Loll, Renate
Starting from the space of Lorentzian metrics, we examine the full gravitational path integral in 3 and 4 space-time dimensions. Inspired by recent results obtained in a regularized, dynamically triangulated formulation of Lorentzian gravity, we gauge-fix to proper-time coordinates and perform a non-perturbative ''''Wick rotation'' on the physical configuration space. Under certain assumptions about the behaviour of the partition function under renormalization, we find that the divergence due to the conformal modes of the metric is cancelled non-perturbatively by a Faddeev-Popov determinant contributing to the effective measure. We illustrate some of our claims by a 3d perturbative calculation.
2001
Article
http://edoc.mpg.de/2716
Nuclear Physics B, v.606, 357-379 (2001)
en
oai:edoc.mpg.de:27192009-03-316:84
Hyperbolic Kac Moody Algebras and Chaos in Kaluza Klein Models
Damour, Thibault
Henneaux, Marc
Julia, Bernard
Nicolai, Hermann
Some time ago, it was found that the never-ending oscillatory chaotic behaviour discovered by Belinsky, Khalatnikov and Lifshitz (BKL) for the generic solution of the vacuum Einstein equations in the vicinity of a spacelike ("cosmological") singularity disappears in spacetime dimensions $D= d+1>10$. Recently, a study of the generalization of the BKL chaotic behaviour to the superstring effective Lagrangians has revealed that this chaos is rooted in the structure of the fundamental Weyl chamber of some underlying hyperbolic Kac-Moody algebra. In this letter, we show that the same connection applies to pure gravity in any spacetime dimension $geq 4$, where the relevant algebras are $AE_d$. In this way the disappearance of chaos in pure gravity models in $D > 10$ dimensions becomes linked to the fact that the Kac-Moody algebras $AE_d$ are no longer hyperbolic for $d > 9$.
2001
Article
http://edoc.mpg.de/2719
urn:ISSN:0370-2693
info:doi/10.1016/S0370-2693(01)00498-1
Physics Letters B, v.509, 323-330 (2001)
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oai:edoc.mpg.de:27222009-03-316:84
Superstring BRST cohomology
Brandt, Friedemann
Kling, Alexander
Kreuzer, Maximilian
We first derive all world-sheet action functionals for NSR superstring models with (1,1) supersymmetry and any number of abelian gauge fields, for gauge transformations of the standard form. Then we prove for these models that the BRST cohomology groups $H^g(s)$, $g<4$ (with the antifields taken into account) are isomorphic to those of the corresponding bosonic string models, whose cohomology is fully known. This implies that the nontrivial global symmetries, Noether currents, background charges, consistent deformations and candidate gauge anomalies of an NSR (1,1) superstring model are in one-to-one correspondence with their bosonic counterparts.
2001
Article
http://edoc.mpg.de/2722
Journal of High Energy Physics, v.08 (2001)
en
oai:edoc.mpg.de:27272009-03-316:84
Exceptional non-renormalization properties and OPE analysis of chiral four-point functions in N=4 SYM_4
Arutyunov, Gleb
Eden, Burkhard U.
Petkou, Anastasios C.
Sokatchev, E.
We show that certain classes of apparently unprotected operators in N=4 SYM_4 do not receive quantum corrections as a consequence of a partial non-renormalization theorem for the 4-point function of chiral primary operators. We develop techniques yielding the asymptotic expansion of the 4-point function of CPOs up to order O(lambda^2) and we perform a detailed OPE analysis. Our results reveal the existence of new non-renormalized operators of approximate dimension 6.
2002
Article
http://edoc.mpg.de/2727
Nuclear Physics B, v.620, 380-404 (2002)
en
oai:edoc.mpg.de:27282009-03-316:84
Open Membranes, p-Brane and Noncommutativity of Boundary String Coordinates
Das, Ashok
Maharana, Jnanadeva
Melikyan, Arsen
We study the dynamics of an open membrane with a cylindrical topology, in the background of a constant three form, whose boundary is attached to p-branes. The boundary closed string is coupled to a two form potential to ensure gauge invariance. We use the action, due to Bergshoeff, London and Townsend, to study the noncommutativity properties of the boundary string coordinates. The constrained Hamiltonian formalism due to Dirac is used to derive the noncommutativity of coordinates. The chain of constraints is found to be finite for a suitable gauge choice, unlike the case of the static gauge, where the chain has an infinite sequence of terms. It is conjectured that the formulation of closed string field theory may necessitate introduction of a star product which is both noncommutative and nonassociative.
2001
Article
http://edoc.mpg.de/2728
Journal of High Energy Physics, v.04, 016 (2001)
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oai:edoc.mpg.de:27312009-03-316:84
Gauge theories of spacetime symmetries
Brandt, Friedemann
Gauge theories of conformal spacetime symmetries are presented which merge features of Yang-Mills theory and general relativity in a new way. The models are local but nonpolynomial in the gauge fields, with a nonpolynomial structure that can be elegantly written in terms of a metric (or vielbein) composed of the gauge fields. General relativity itself emerges from the construction as a gauge theory of spacetime translations. The role of the models within a general classification of consistent interactions of gauge fields is discussed as well.
2001
Article
http://edoc.mpg.de/2731
Physical Review D, v.64, 065025 (2001)
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oai:edoc.mpg.de:27322009-03-316:84
Quantum corrections for (anti)-evaporating black hole
Buric, Maja
Radovanovic, Voja
In this paper we analyse the quantum correction for Schwarzschild black hole in the Unruh state in the framework of spherically symmetric gravity (SSG) model. SSG is a two-dimensional dilaton model which is obtained by spherically symmetric reduction from the four-dimensional theory. We find the one-loop geometry of the (anti)-evaporating black hole and corrections for mass, entropy and apparent horizon.
2001
Article
http://edoc.mpg.de/2732
Physical Review D, v.63, 044020 (2001)
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oai:edoc.mpg.de:27342009-03-316:84
Infinite Kinematic Self-Similarity and Perfect Fluid Spacetimes
Sintes, Alicia M.
Benoit, Patricia M.
Coley, Alan A.
Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary differential equations. The qualitative properties of solutions of this system of equations, and in particular their asymptotic behavior, are studied. Special cases, including some of the invariant sets and the geodesic case, are examined in detail and the exact solutions are provided. The class of solutions exhibiting physical self-similarity are found to play an important role in describing the asymptotic behavior of the infinite kinematic self-similar models.
2001
Article
http://edoc.mpg.de/2734
General Relativity and Gravitation, v.33, 1863-1895 (2001)
en
oai:edoc.mpg.de:27352009-03-316:84
Dynamically Triangulating Lorentzian Quantum Gravity
Ambjörn, Jan
Jurkiewicz, Jerzy
Loll, Renate
Fruitful ideas on how to quantize gravity are few and far between. In this paper, we give a complete description of a recently introduced non-perturbative gravitational path integral whose continuum limit has already been investigated extensively in d < 4, with promising results. It is based on a simplicial regularization of Lorentzian spacetimes and, most importantly, possesses a well-defined, non-perturbative Wick rotation. We present a detailed analysis of the geometric and mathematical properties of the discretized model in d = 3, 4. This includes a derivation of Lorentzian simplicial manifold constraints, the gravitational actions and their Wick rotation. We define a transfer matrix for the system and show that it leads to a well-defined self-adjoint Hamiltonian. In view of numerical simulations, we also suggest sets of Lorentzian Monte Carlo moves. We demonstrate that certain pathological phases found previously in Euclidean models of dynamical riangulations cannot be realized in the Lorentzian case. (C) 2001 Elsevier Science B.V. All rights reserved
2001
Article
http://edoc.mpg.de/2735
Nuclear Physics B, v.610, 347-382 (2001)
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oai:edoc.mpg.de:27382009-03-316:84
Boundary Superstring Field Theory Annulus Partition Function in the Presence of Tachyons
Arutyunov, Gleb
Pankiewicz, Ari
Stefanski, Bogdan
We compute the Boundary Superstring Field Theory partition function on the annulus in the presence of independent linear tachyon profiles on the two boundaries. The R-R sector is found to contribute non-trivially to the derivative terms of the space-time effective action. In the process we construct a boundary state description of D-branes in the presence of a linear tachyon. We quantize the open string in a tachyonic background and address the question of open/closed string duality.
2001
Article
http://edoc.mpg.de/2738
Journal of High Energy Physics, v.06, 049 (2001)
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oai:edoc.mpg.de:27392009-03-316:84
On nonrenormalization and OPE in superconformal field theories
Arutyunov, Gleb
Eden, Burkhard U.
Sokatchev, E.
The OPE of two N=2 R-symmetry current (short) multiplets is determined by the possible superspace three-point functions that two such multiplets can form with a third, a priori long multiplet. We show that the shortness conditions on the former put strong restrictions on the quantum numbers of the latter. In particular, no anomalous dimension is allowed unless the third supermultiplet is an R-symmetry singlet. This phenomenon should explain many known non-renormalization properties of correlation functions, including the one of four stress-tensor multiplets in N=4 SYM_4
2001
Article
http://edoc.mpg.de/2739
Nuclear Physics B, v.619, 359-372 (2001)
en
oai:edoc.mpg.de:27402009-03-316:84
Lorentzian 3d gravity with wormholes via matrix models
Ambjörn, Jan
Jurkiewicz, Jerzy
Loll, Renate
Vernizzi, Graziano
We uncover a surprising correspondence between a non-perturbative formulation of three-dimensional Lorentzian quantum gravity and a hermitian two-matrix model with ABAB-interaction. The gravitational transfer matrix can be expressed as the logarithm of a two-matrix integral, and we deduce from the known structure of the latter that the model has two phases. In the phase of weak gravity, well-defined two-dimensional universes propagate in proper time, whereas in the strong-coupling phase the spatial hypersurfaces disintegrate into many components connected by wormhole
2001
Article
http://edoc.mpg.de/2740
Journal of High Energy Physics, v.09, 022 (2001)
en
oai:edoc.mpg.de:27422009-03-316:84
N=8 matter coupled AdS_3 supergravities
Nicolai, Hermann
Samtleben, Henning
Following the recent construction of maximal (N=16) gauged supergravity in three dimensions, we derive gauged D=3, N=8 supergravities in three dimensions as deformations of the corresponding ungauged theories with scalar manifolds SO(8,n)/(SO(8)x SO(n)). As a special case, we recover the N=(4,4) theories with local SO(4) = SO(3)_L x SO(3)_R, which reproduce the symmetries and massless spectrum of D=6, N=(2,0) supergravity compactified on AdS_3 x S^3.
2001
Article
http://edoc.mpg.de/2742
urn:ISSN:0370-2693
info:doi/10.1016/S0370-2693(01)00779-1
Physics Letters B, v.514, 165-172 (2001)
en
oai:edoc.mpg.de:27502009-04-026:84
On spacetime supersymmetry and string duality in nine dimensions
Abou-Zeid, Mohab
Nicolai, Hermann
N = 2 extended space-time supersymmetry in nine dimensions implies that the BPS states corresponding to momentum and winding of either of the type-II superstrings compactified on S1 transform as inequivalent supermultiplets. This fact can be checked using world-sheet techniques, and provides the physical basis for the connection between IIA superstring theory compactified on a circle of radius R and IIB theory compactified on a circle of radius 1/R. Aspects of the duality between M-theory compactified on T2 and IIB theory compactified on S1 follow from the structure of N = 2, D = 9 supergravity. The coupling of N = 2, D = 9 supergravity to the BPS states is also discussed.
2000
Article
http://edoc.mpg.de/2750
urn:ISSN:0920-5632
info:doi/10.1016/S0920-5632(00)00765-9
Nuclear Physics B, v.88, 168-174 (2000)
en
oai:edoc.mpg.de:27532009-03-316:84
Colliding String Waves and Duality
Das, Ashok
Maharana, Jnanadeva
Melikyan, Arsen
The collision of plane waves corresponding to massless states of closed string is considered in D-dimensional spaceŻtime. The reduced tree level effective action is known to be manifestly O(d,d) invariant, d being the number of transverse spatial dimensions in the collision process. We adopt a coset space reformulation of the effective two-dimensional theory and discuss the relation of this process with classical integrable systems in two dimensions in the presence of gravity. We show how it is possible to generate new backgrounds for the scattering process, from known background solutions to the equations of motion, in the coset reformulation. We present explicit calculations for the case of four spaceŻtime dimensions as an illustrative example.
2001
Article
http://edoc.mpg.de/2753
Physics Letters B, v.518, 306-314 (2001)
en
oai:edoc.mpg.de:27552009-03-316:84
Open Strings in Simple Current Orbifolds
Matsubara, Keizo
Schomerus, Volker
Smedbäck, Mikael
We study A(b)(a) branes and open strings in a large class of orbifold backgrounds using microscopic techniques of boundary conformal field theory. In particular, we obtain factorizing operator product expansions of open string vertex operators for such branes. Applications include branes in Z(2) orbifolds of the SU(2) WZW model and in the D-series of unitary minimal models considered previously by Runkel.
2002
Article
http://edoc.mpg.de/2755
Nuclear Physics B, v.626, 53-72 (2002)
en
oai:edoc.mpg.de:27572009-05-286:84
Two Loops to Two Loops in N=4 Supersymmetric Yang-Mills Theory
Plefka, Jan
Staudacher, Matthias
We present a full two-loop (g6) perturbative field theoretic calculation of the expectation value of two circular Maldacena-Wilson loops in D = 4 = 4 supersymmetric U(N) gauge theory. It is demonstrated that, after taking into account very subtle cancellations of bulk and boundary divergences, the result is completely finite without any renormalization. As opposed to previous lower order calculations existing in the literature, internal vertex diagrams no longer cancel identically and lead to subleading corrections to the dominant ladder diagrams. Taking limits, we proceed to extract the two-loop static potential corresponding to two infinite anti-parallel lines. Our result gives some evidence that the existing strong-coupling calculations using the AdS/CFT conjecture might sum up the full set of large N planar Feynman diagrams.
2001
Article
http://edoc.mpg.de/2757
Journal of High Energy Physics, v.09 (2001)
en
oai:edoc.mpg.de:27582009-03-316:84
On D0-branes in Gepner models
Scheidegger, Emanuel
We show why and when D0-branes at the Gepner point of Calabi-Yau manifolds given as Fermat hypersurfaces exist.
2002
Article
http://edoc.mpg.de/2758
Journal of High Energy Physics, v.08, 001 (2002)
en
oai:edoc.mpg.de:27632009-03-316:84
Dirichlet Branes on Orientifolds
Quiroz, N.
Stefanski, Bogdan
We consider the classification of BPS and non-BPS D-branes in orientifold models. In particular we construct all stable BPS and non-BPS D-branes in the Gimon-Polchinski (GP) and Dabholkar-Park-Blum-Zaffaroni (DPBZ) orientifolds and determine their stability regions in moduli space as well as decay products. We find several kinds of integrally and torsion charged non-BPS D-branes. Certain of these are found to have projective representations of the orientifold×GSO group on the Chan-Paton factors. It is found that the GP orientifold is not described by equivariant orthogonal K-theory as may have been at first expected. Instead a twisted version of this K-theory is expected to be relevant.
2002
Article
http://edoc.mpg.de/2763
Physical Review D, v.66 (2002)
en
oai:edoc.mpg.de:27662009-03-316:84
A Lorentzian Cure for Euclidean Troubles
Ambjörn, Jan
Dasgupta, Arundhati
Jurkiewicz, Jerzy
Loll, Renate
There is strong evidence coming from Lorentzian dynamical triangulations that the unboundedness of the gravitational action is no obstacle to the construction of a well-defined non-perturbative path integral. In a continuum approach, a similar suppression of the conformal divergence comes about as the result of a non-trivial path-integral measure.
2002
Article
http://edoc.mpg.de/2766
Nuclear Physics B Proc. Suppl., v.106, 977-979 (2002)
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oai:edoc.mpg.de:27672009-03-316:84
Boundary Liouville Field theory : boundary three point function
Ponsot, Benedicte
Teschner, Jörg
Liouville field theory is considered on domains with conformally invariant boundary conditions. We present an explicit expression for the three-point function of boundary fields in terms of the fusion coefficients which determine the monodromy properties of the conformal blocks.
2002
Article
http://edoc.mpg.de/2767
Nuclear Physics B, v.622, 309-327 (2002)
en
oai:edoc.mpg.de:27702009-03-316:84
Branching rules of semi-simple Lie algebras using affine extensions
Quella, Thomas
We present a closed formula for the branching coefficients of an embedding [fraktur p] [hookrightarrow] [fraktur g] of two finite-dimensional semi-simple Lie algebras. The formula is based on the untwisted affine extension of [fraktur p] . It leads to an alternative proof of a simple algorithm for the computation of branching rules, which is an analogue of the Racah-Speiser algorithm for tensor products. We present some simple applications and describe how integral representations for branching coefficients can be obtained. In the last part, we comment on the relation of our approach to the theory of NIM-reps of the fusion ring in WZW models with chiral algebra [{mathfrak g}}_k] . In fact, it turns out that for these models each embedding [fraktur p] [hookrightarrow] [fraktur g] induces a NIM-rep at level k [rightarrow] [infty] . In cases where these NIM-reps can be extended to finite level, we obtain a Verlinde-like formula for branching coefficients. Reviewing this question, we propose a solution to a puzzle which remained open in related work by Alekseev, Fredenhagen, Quella and Schomerus.
2002
Article
http://edoc.mpg.de/2770
Journal of Physics A, v.35, 3743-3753 (2002)
en
oai:edoc.mpg.de:27712009-03-316:84
D-branes in coset models
Fredenhagen, Stefan
Schomerus, Volker
The analysis of D-branes in coset models G/H provides a natural extension of recent studies on branes in WZW-theory and it has various interesting applications to physically relevant models. In this work we develop a reduction procedure that allows to construct the non-commutative gauge theories which govern the dynamics of branes in G/H. We obtain a large class of solutions and interpret the associated condensation processes geometrically. The latter are used to propose conservation laws for the dynamics of branes in coset models at large level k. In super-symmetric theories, conserved charges are argued to take their values in the representation ring of the denominator theory. Finally, we apply the general results to study boundary fixed points in two examples, namely for parafermions and minimal models.
2002
Article
http://edoc.mpg.de/2771
Journal of High Energy Physics, v.02 (2002)
en
oai:edoc.mpg.de:27732009-03-316:84
Implications of Superconformal Symmetry for Interacting (2,0) Tensor Multiplets
Arutyunov, Gleb
Sokatchev, E.
We study the structure of the four-point correlation function of the lowest-dimension 1/2 BPS operators (stress-tensor multiplets) in the (2,0) six-dimensional theory. We first discuss the superconformal Ward identities and the group-theoretical restrictions on the corresponding OPE. We show that the general solution of the Ward identities is expressed in terms of a single function of the two conformal cross-ratios ("prepotential"). Using the maximally extended gauged seven-dimensional supergravity, we then compute the four-point amplitude in the supergravity approximation and identify the corresponding prepotential. We analyze the leading terms in the OPE by performing a conformal partial wave expansion and show that they are in agreement with the non-renormalization theorems following from representation theory. The investigation of the (2,0) theory is carried out in close parallel with the familiar four-dimensional [View Image] super-Yang?Mills theory
2002
Article
http://edoc.mpg.de/2773
Nuclear Physics B, v.635, 3-32 (2002)
en
oai:edoc.mpg.de:27742009-03-316:84
Limiting Geometries of Two Circular Maldacena-Wilson Loop Operators
Arutyunov, Gleb
Plefka, Jan
Staudacher, Matthias
We further analyze a recent perturbative two-loop calculation of the expectation value of two axi-symmetric circular Maldacena-Wilson loops in [Script N] = 4 gauge theory. Firstly, it is demonstrated how to adapt the previous calculation of anti-symmetrically oriented circles to the symmetric case. By shrinking one of the circles to zero size we then explicitly work out the first few terms of the local operator expansion of the loop. Our calculations explicitly demonstrate that circular Maldacena-Wilson loops are non-BPS observables precisely due to the appearance of unprotected local operators. The latter receive anomalous scaling dimensions from non-ladder diagrams. Finally, we present new insights into a recent conjecture claiming that coincident circular Maldacena-Wilson loops are described by a gaussian matrix model. We report on a novel, supporting two-loop test, but also explain and illustrate why the existing arguments in favor of the conjecture are flawed.
2001
Article
http://edoc.mpg.de/2774
Journal of High Energy Physics, v.12, 014 (2001)
en
oai:edoc.mpg.de:27782009-03-316:84
Fivebranes Wrapped on SLAG Three-Cycles and Related Geometry
Gauntlett, Jerome P.
Kim, Nakwoo
Martelli, Dario
Waldram, Daniel
We construct ten-dimensional supergravity solutions corresponding to the near horizon limit of IIB fivebranes wrapping special lagrangian three-cycles of constant curvature. The case of branes wrapping a three-sphere provides a gravity dual of pure [Script N] = 2 super--Yang-Mills theory in D = 3. The non-trivial part of the solutions are seven manifolds that admit two G2 structures each of which is covariantly constant with respect to a different connection with torsion. We derive a formula for the generalised calibration for this general class of solutions. We discuss analogous aspects of the geometry that arises when fivebranes wrap other supersymmetric cycles which lead to Spin(7) and SU(N) structures. In some cases there are two covariantly constant structures and in others one.
2001
Article
http://edoc.mpg.de/2778
Journal of High Energy Physics, v.11, 018 (2001)
en
oai:edoc.mpg.de:27792009-03-316:84
Branes in the Euclidean AdS_3
Ponsot, Benedicte
Schomerus, Volker
Teschner, Jörg
In this work we propose an exact microscopic description of maximally symmetric branes in a euclidean AdS3 background. As shown by Bachas and Petropoulos, the most important such branes are localized along a euclidean AdS2 [subset] AdS3. We provide explicit formulas for the coupling of closed strings to such branes (boundary states) and for the spectral density of open strings. The latter is computed in two different ways first in terms of the open string reflection amplitude and then also from the boundary states by world-sheet duality. This gives rise to an important Cardy type consistency check. All the results are compared in detail with the geometrical picture. We also discuss a second class of branes with spherical symmetry and finally comment on some implications for D-branes in a 2D back hole geometry
2002
Article
http://edoc.mpg.de/2779
Journal of High Energy Physics, v.02 (2002)
en
oai:edoc.mpg.de:27822009-04-026:84
A non-perturbative Lorentzian path integral for gravity
Ambjörn, Jan
Jurkiewicz, Jerzy
Loll, Renate
We construct a well-defined regularized path integral for Lorentzian quantum gravity in terms of dynamically triangulated causal space-times. Each Lorentzian geometry and its action have a unique Wick rotation to the Euclidean sector. All space-time histories possess a distinguished notion of a discrete proper time and, for finite lattice volume, the associated transfer matrix is self-adjoint, bounded, and strictly positive. The degenerate geometric phases found in dynamically triangulated Euclidean gravity are not present.
2000
Article
http://edoc.mpg.de/2782
Physical Review Letters, v.85, 924-927 (2000)
en
oai:edoc.mpg.de:27832009-04-026:84
Supersymmetric effective action of Matrix theory
Nicolai, Hermann
Plefka, Jan
We present a simple derivation of the supersymmetric one-loop effective action of SU(2) Matrix theory by expressing it in a compact exponential form whose invariance under supersymmetry transformations is obvious. This result clarifies the one-loop exactness of the leading (v2)2 interactions and the absence of non-perturbative corrections.
2000
Article
http://edoc.mpg.de/2783
urn:ISSN:0370-2693
info:doi/10.1016/S0370-2693(00)00210-0
Physics Letters B, v.477, 309-312 (2000)
en
oai:edoc.mpg.de:27892009-04-026:84
An exceptional geometry for d=11 supergravity?
Koepsell, Kilian
Nicolai, Hermann
Samtleben, Henning
We analyse the algebraic constraints of the generalized vielbein in SO(1,2)×SO(16) invariant d = 11 supergravity, and show that the bosonic degrees of freedom of d = 11 supergravity, which become the physical ones upon reduction to d = 3, can be assembled into an E8(8)-valued vielbein already in 11 dimensions. A crucial role in the construction is played by the maximal nilpotent commuting subalgebra of E8(8), of dimension 36, suggesting a partial unification of general coordinate and tensor gauge transformations.
2000
Article
http://edoc.mpg.de/2789
urn:ISSN:0264-9381
info:doi/10.1088/0264-9381/17/18/308
Classical and Quantum Gravity, v.17, 3689-3702 (2000)
en
oai:edoc.mpg.de:27952009-04-026:84
Vertex Operators for the Supermembrane
Dasgupta, Arundhati
Nicolai, Hermann
Plefka, Jan
We derive the vertex operators that are expected to govern the emission of the massless d = 11 supermultiplet from the supermembrane in the light cone gauge. We demonstrate that they form a representation of the supersymmetry algebra and reduce to the type-IIA superstring vertex operators under double-dimensional reduction, as well as to the vertices of the d = 11 superparticle in the point-particle limit. As a byproduct, our results can be used to derive the corresponding vertex operators for matrix theory and to describe its linear coupling to an arbitrary d = 11 supergravity background. Possible applications are discussed.
2000
Article
http://edoc.mpg.de/2795
urn:ISSN:1126-6708
info:doi/10.1088/1126-6708/2000/05/007
Journal of High Energy Physics, v.05 (2000)
en
oai:edoc.mpg.de:27972009-04-026:84
Yang-Mills Integrals for Orthogonal, Symplectic and Exceptional Groups
Krauth, Werner
Staudacher, Matthias
We apply numerical and analytic techniques to the study of YangŻ Mills integrals with orthogonal, symplectic and exceptional gauge symmetries. The main focus is on the supersymmetric integrals, which correspond essentially to the bulk part of the Witten index for susy quantum mechanical gauge theory. We evaluate these integrals for D=4 and group rank up to three, using Monte Carlo methods. Our results are at variance with previous findings. We further compute the integrals with the deformation technique of Moore, Nekrasov and Shatashvili, which we adapt to the groups under study. Excellent agreement with all our numerical calculations is obtained. We also discuss the convergence properties of the purely bosonic integrals.
2000
Article
http://edoc.mpg.de/2797
Nuclear Physics B, v.584, 641-655 (2000)
en
oai:edoc.mpg.de:27992009-03-316:84
Quantum spin dynamics (QSD): VII. Symplectic structures and continuum lattice formulations of gauge field theories
Thiemann, Thomas
Interesting nonlinear functions on the phase spaces of classical field theories can never be quantized immediately because the basic fields of the theory become operator-valued distributions. Therefore, one is usually forced to find a smeared substitute for such a function which corresponds to a regularization. The smeared functions define a new symplectic manifold of their own which is easy to quantize. Finally, one must remove the regulator and establish that the final operator, if it exists, has the correct classical limit.
In this paper we begin the investigation of these steps for diffeomorphism-invariant quantum field theories of connections. We introduce a (generalized) projective family of symplectic manifolds, coordinatized by the smeared fields, which is labelled by a pair consisting of a graph and another graph dual to it. We show that a subset of the corresponding projective limit can be identified with the symplectic manifold that one started from. Then we illustrate the programme outlined above by applying it to the Gauss constraint.
This paper also complements, as a side result, earlier work by Ashtekar, Corichi and Zapata who observed that certain operators are non-commuting on certain states, although the Poisson brackets between the corresponding classical functions vanish. These authors showed that this is not a contradiction provided that one refrains from a phase space quantization but rather applies a quantization based on the Lie algebra of vector fields on the configuration space of the theory. Here we show that one can provide a phase space quantization, that is, one can find other functions on the classical phase space which give rise to the same operators but whose Poisson algebra precisely mirrors the quantum commutator algebra.
The framework developed here is the classical cornerstone on which the semiclassical analysis in a new series of papers called ''gauge theory coherent states' is based.
2001
Article
http://edoc.mpg.de/2799
Classical and Quantum Gravity, v.18, 3293-3338 (2001)
en
oai:edoc.mpg.de:28002009-03-316:84
Gauge field theory coherent states (GCS): I. General properties
Thiemann, Thomas
In this paper we outline a rather general construction of diffeomorphism covariant coherent states for quantum gauge theories. By this we mean states [psi] (A,E), labelled by a point (A,E) in the classical phase space, consisting of canonically conjugate pairs of connections A and electric fields E, respectively, such that: (a) they are eigenstates of a corresponding annihilation operator which is a generalization of A-iE smeared in a suitable way; (b) normal ordered polynomials of generalized annihilation and creation operators have the correct expectation value; (c) they saturate the Heisenberg uncertainty bound for the fluctuations of [hat A] , [hat E] ; and (d) they do not use any background structure for their definition, that is, they are diffeomorphism covariant.
This is the first paper in a series of articles entitled ''Gauge field theory coherent states (GCS)' which aims to connect non-perturbative quantum general relativity with the low-energy physics of the standard model. In particular, coherent states enable us for the first time to take into account quantum metrics which are excited everywhere in an asymptotically flat spacetime manifold as is needed for semiclassical considerations.
The formalism introduced in this paper is immediately applicable also to lattice gauge theory in the presence of a (Minkowski) background structure on a possibly infinite lattice.
2001
Article
http://edoc.mpg.de/2800
Classical and Quantum Gravity, v.18, 2025-2064 (2001)
oai:edoc.mpg.de:28012009-03-316:84
Gauge field theory coherent states (GCS): II. Peakedness properties
Thiemann, Thomas
Winkler, Oliver
In this paper we apply the methods outlined in the previous paper of this series to the particular set of states obtained by choosing the complexifier to be a Laplace operator for each edge of a graph. The corresponding coherent state transform was introduced by Hall for one edge and generalized by Ashtekar, Lewandowski, Marolf, Mourăo and Thiemann to arbitrary, finite, piecewise-analytic graphs.
However, both of these works were incomplete with respect to the following two issues.
The focus was on the unitarity of the transform and left the properties of the corresponding coherent states themselves untouched.
While these states depend in some sense on complexified connections, it remained unclear what the complexification was in terms of the coordinates of the underlying real phase space.
In this paper we complement these results: first, we explicitly derive the complexification of the configuration space underlying these heat kernel coherent states and, secondly, prove that this family of states satisfies all the usual properties.
(i) Peakedness in the configuration, momentum and phase space (or Bargmann-Segal) representation.
(ii) Saturation of the unquenched Heisenberg uncertainty bound.
(iii) (Over)completeness.
These states therefore comprise a candidate family for the semiclassical analysis of canonical quantum gravity and quantum gauge theory coupled to quantum gravity. They also enable error-controlled approximations to difficult analytical calculations and therefore set a new starting point for numerical, semiclassical canonical quantum general relativity and gauge theory.
The text is supplemented by an appendix which contains extensive graphics in order to give a feeling for the so far unknown peakedness properties of the states constructed.
2001
Article
http://edoc.mpg.de/2801
Classical and Quantum Gravity, v.18, 2561-2636 (2001)
en
oai:edoc.mpg.de:28022009-03-316:84
Gauge field theory coherent states (GCS): III. Ehrenfest theorems
Thiemann, Thomas
Winkler, Oliver
In the preceding paper of this series of articles we established peakedness properties of a family of coherent states that were introduced by Hall for any compact gauge group and were later generalized to gauge field theory by Ashtekar, Lewandowski, Marolf, Mourăo and Thiemann.
In this paper we establish the ''Ehrenfest property' of these states which are labelled by a point (A,E), a connection and an electric field, in the classical phase space. By this we mean that the expectation values of the elementary operators (and of their commutators divided by i [hbar] , respectively) in a coherent state labelled by the (A,E) are, to zeroth order in [hbar] , given by the values of the corresponding elementary functions (and of their Poisson brackets, respectively) at the point (A,E).
These results can be extended to all polynomials of elementary operators and to a certain non-polynomial function of the elementary operators associated with the volume operator of quantum general relativity. These findings are another step towards establishing that the infinitesimal quantum dynamics of quantum general relativity might, to lowest order in [hbar] , indeed be given by classical general relativity.
2001
Article
http://edoc.mpg.de/2802
Classical and Quantum Gravity, v.18, 4629-4681 (2001)
en
oai:edoc.mpg.de:28032009-03-316:84
Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamical limit
Thiemann, Thomas
Winkler, Oliver
In the canonical approach to Lorentzian quantum general relativity in four spacetime dimensions an important step forward has been made by Ashtekar, Isham and Lewandowski some eight years ago through the introduction of a Hilbert space structure, which was later proved to be a faithful representation of the canonical commutation and adjointness relations of the quantum field algebra of diffeomorphism invariant gauge field theories by Ashtekar, Lewandowski, Marolf, Mourăo and Thiemann. This Hilbert space, together with its generalization due to Baez and Sawin, is appropriate for semi-classical quantum general relativity if the spacetime is spatially compact. In the spatially non-compact case, however, an extension of the Hilbert space is needed in order to approximate metrics that are macroscopically nowhere degenerate. For this purpose, in this paper we apply the theory of the infinite tensor product (ITP) of Hilbert Spaces, developed by von Neumann more than sixty years ago, to quantum general relativity. The cardinality of the number of tensor product factors can take the value of any possible Cantor aleph, making this mathematical theory well suited to our problem in which a Hilbert space is attached to each edge of an arbitrarily complicated, generally infinite graph. The new framework opens access to a new arsenal of techniques, appropriate to describe fascinating physics such as quantum topology change, semi-classical quantum gravity, effective low-energy physics etc from the universal point of view of the ITP. In particular, the study of photons and gravitons propagating on fluctuating quantum spacetimes should now be in reach.
2001
Article
http://edoc.mpg.de/2803
Classical and Quantum Gravity, v.18, 4997-5053 (2001)
en
oai:edoc.mpg.de:28042009-04-026:84
Currents and Superpotentials in classical gauge theories: II. Global aspects and the example of Affine gravity
Julia, Bernard
Silva, Sebastian
The conserved charges associated with gauge symmetries are defined at a boundary component of spacetime because the corresponding Noether current can be rewritten on-shell as the divergence of a superpotential. However, the latter is afflicted by ambiguities. Regge and Teitelboim found a procedure to lift the arbitrariness in the Hamiltonian framework. An alternative covariant formula was proposed by one of us for an arbitrary variation of the superpotential, it depends only on the equations of motion and on the gauge symmetry under consideration. Here we emphasize that in order to compute the charges, it is enough to stay at a boundary of spacetime, without requiring any hypothesis about the bulk or about other boundary components, so one may speak of holographic charges. It is well known that the asymptotic symmetries
that lead to conserved charges are really defined at infinity, but the choice of boundary conditions and surface terms in the action and in the charges is usually determined
through integration by parts, whereas each component of the boundary should be considered separately. We treat the example of gravity (for any spacetime dimension, with
or without cosmological constant), formulated as an affine theory which is a natural generalization of the Palatini and Cartan-Weyl (vielbein) first-order formulations. We then
show that the superpotential associated with a Dirichlet boundary condition on the metric (the one needed to treat asymptotically flat or AdS spacetimes) is the one proposed
by Katz et al and not that of Komar. We finally discuss the KBL superpotential at null infinity.
2000
Article
http://edoc.mpg.de/2804
Classical and Quantum Gravity, v.17, 4733-4744 (2000)
en
oai:edoc.mpg.de:28082009-04-026:84
Bulk Witten Indices and the Number of Normalizable Ground States in Supersymmetric Quantum Mechanics of Orthogonal, Symplectic and Exceptional Groups
Staudacher, Matthias
This note addresses the question of the number of normalizable vacuum states in supersymmetric quantum mechanics with sixteen supercharges and arbitrary semi-simple compact gauge group, up to rank three. After evaluating certain contour integrals obtained by appropriately adapting BRST deformation techniques we propose novel rational values for the bulk indices. Our results demonstrate that an asymptotic method for obtaining the boundary contribution to the index, originally due to Green and Gutperle, fails for groups other than SU(N). We then obtain likely values for the number of ground states of these systems. In the case of orthogonal and symplectic groups our finding is consistent with recent conjectures of Kac and Smilga, but appears to contradict their result in the case of the
exceptional group G2.
2000
Article
http://edoc.mpg.de/2808
Physics Letters B, v.488, 194-198 (2000)
en
oai:edoc.mpg.de:29572009-04-026:84
Brane dynamics in CFT backgrounds
Fredenhagen, Stefan
Schomerus, Volker
In this note we discuss bound states of un- or meta-stable brane configurations in various non-trivial (curved) backgrounds. We begin by reviewing some known results concerning brane dynamics on group manifolds. These are then employed to study condensation in cosets of the WZW model. While the basic ideas are more general, our presentation focuses on parafermion theories and, closely related, $N=2$ superconformal minimal models. We determine the (non-commutative) low energy effective actions for all maximally symmetric branes in a decoupling limit of the two theories. These actions are used to show that the lightest branes can be regarded as elementary constituents for all other maximally symmetric branes.
Other
http://edoc.mpg.de/2957
en
oai:edoc.mpg.de:30292009-03-316:84
D-branes, Orientifolds and K-theory
Stefanski, Bogdan
The complete D-brane spectrum in Z(2) orientifolds is computed. Stable non-BPS D-branes with both integral and torsion charges are found. The relation to K-theory is discussed and a new K-theory relevant to orientifolds is suggested.
2002
Article
http://edoc.mpg.de/3029
Fortschritte der Physik, v.50, 986-991 (2002)
en
oai:edoc.mpg.de:30302009-03-316:84
Some stationary points of gauged N=16 D=3 supergravity
Fischbacher, Thomas
Five nontrivial stationary points are found for maximal gauged N = 16 supergravity in three dimensions with gauge group SO(8) x SO(8) by restricting the potential to a submanifold of the space of SU(3) subset of (SO(8) x SO(8))(diag) singlets. The construction presented here uses the embedding of E7(+7) subset of E8(+8) to lift the analysis of N = 8, D = 4 supergravity performed by N. Warner to N = 16, D = 3, and hence, these stationary points correspond to some of the known extrema of gauged N = 8, D = 4 supergravity
2002
Article
http://edoc.mpg.de/3030
Nuclear Physics B, v.638, 207-219 (2002)
en
oai:edoc.mpg.de:30372009-03-316:84
UV/IR Mixing via Closed Strings and Tachyonic Instabilities
Armoni, Adi
Lopez, Esperanza
We discuss UV/IR mixing effects in non-supersymmetric non-commutative U(N) gauge theories. We show that the singular (non-planar) terms in the 2- and 3-point functions, namely the poles and the logarithms, can be obtained from a manifestly gauge invariant effective action. The action. which involves open Wilson line operators, can be derived front closed strings exchange between two stacks of D-branes. Our concrete example is type 0B string theory and the field theory that lives on a collection of N electric D3-branes. We show that one of the closed string modes that couple to the field theory operator which is responsible for the infrared poles, is the type 0 tachyon
2002
Article
http://edoc.mpg.de/3037
Nuclear Physics B, v.632, 240-256 (2002)
en
oai:edoc.mpg.de:30382009-03-316:84
The Real Wick Rotations in Quantum Gravity
Dasgupta, Arundhati
We discuss Wick rotations in the context of gravity, with emphasis on a non-perturbative Wick rotation proposed in hep-th/0103186 mapping real lorentzian metrics to real euclidean metrics in proper-time coordinates. As an application, we demonstrate how this Wick rotation leads to a correct answer for a two dimensional non-perturbative path-integral.
2002
Article
http://edoc.mpg.de/3038
Journal of High Energy Physics, v.07 (2002)
en
oai:edoc.mpg.de:30392009-03-306:84
The light cone open supermembrane
Dasgupta, Arundhati
Nicolai, Hermann
Plefka, Jan
We review aspects of the light-cone quantisation of the 11-dimensional supermembrane world volume theory. We explicitly construct vertex operators for the massless states of the eleven dimensional supergraviton multiplet and study their interactions. The open supermembrane and its vertex operators are also discussed. Moreover we show how our results have direct applications to Matrix theory by the appropriate regularisation of the supermembrane.
De Boeck
2003
Conference-Paper
http://edoc.mpg.de/3039
Henneaux, Marc; Sevrin, Alexander: Strings and Gravity, De Boeck, 83-98 (2003)
en
oai:edoc.mpg.de:30412009-03-316:84
M-theory solutions with AdS factors
Gauntlett, Jerome P.
Kim, Nakwoo
Pakis, Stathis
Waldram, Daniel
Solutions of D = 7 maximal gauged supergravity are constructed with metrics that are a product of an n-dimensional anti-de Sitter (AdS) space, with n = 2, 3, 4, 5, and certain Einstein manifolds. The gauge fields have the same form as in the recently constructed solutions describing the near-horizon limits of M5-branes wrapping supersymmetric cycles. The new solutions do not preserve any supersymmetry and can be uplifted to obtain new solutions of D = 11 supergravity, which are warped and twisted products of the D = 7 metric with a squashed four-sphere. Some aspects of the stability of the solutions are discussed
2002
Article
http://edoc.mpg.de/3041
Classical and Quantum Gravity, v.19, 3927-3945 (2002)
oai:edoc.mpg.de:30432009-04-286:84
Superstring on pp-wave orbifold from large N quiver gauge theory
Kim, Nakwoo
Pankiewicz, Ari
Rey, Soo-Jong
Theisen, Stefan
We extend the proposal of Berenstein, Maldacena and Nastase to the Type IIB superstring propagating on a pp-wave over the R-4/Z(k) Orbifold. We show that first-quantized free string theory is described correctly by the large-N, fixed gauge coupling limit of N = 2 [U(N)](k) quiver gauge theory. We propose a precise. map between gauge theory operators and string states for both untwisted and twisted sectors. We also compute leading-order perturbative correction to the anomalous dimensions of these operators. The result is in agreement with the value deduced from the string energy spectrum, thus substantiating our proposed operator-state map
2002
Article
http://edoc.mpg.de/3043
urn:ISSN:1434-6052
info:doi/10.1007/s10052-002-0986-y
European Physical Journal C, v.25, 327-332 (2002)
oai:edoc.mpg.de:30462009-03-316:84
An algorithm for twisted fusion rules
Quella, Thomas
Runkel, Ingo
Schweigert, Christoph
We present an algorithm for an efficient calculation of the fusion rules of twisted representations of untwisted affine Lie algebras. These fusion rules appear as annulus coefficients in boundary WZW theories and provide NIM-reps of the WZW fusion rules.
2002
Article
http://edoc.mpg.de/3046
Advances in Theoretical and Mathematical Physics, v.6, 197-205 (2002)
en
oai:edoc.mpg.de:30502009-03-316:84
Nonplanar Anomalies in Noncommutative Theories and the Green-Schwarz Mechanism
Armoni, Adi
Lopez, Esperanza
Theisen, Stefan
We discuss nonplanar anomalies in noncommutative gauge theories. In particular we show that a nonplanar anomaly exists when the external noncommutative momentum is zero and that it leads to a non-conservation of the associated axial charge. In the case of nonplanar local anomalies, a cancellation of the anomaly can be achieved by a Green-Schwarz mechanism . In an example of D3 branes placed on an orbifold singularity that leads to a chiral theory, the mechanism involves twisted RR fields which propagate with zero noncommutative momentum. Global anomalies are not cancelled and, in particular, the decay pi(0) --> 2gamma is allowed
2002
Article
http://edoc.mpg.de/3050
urn:ISSN:1029-8479
info:doi/10.1088/1126-6708/2002/06/050
Journal of High Energy Physics, v.6 (2002)
en
oai:edoc.mpg.de:30512009-03-316:84
Symmetry Breaking Boundary States and Defect Lines
Quella, Thomas
Schomerus, Volker
We present a large and universal class of new boundary states which break part of the chiral symmetry in the underlying bulk theory. Our formulas are based on coset constructions and they can be regarded as a non-abelian generalization of the ideas that were used by Maldacena, Moore and Seiberg to build new boundary states for SU(N). We apply our expressions to construct defect lines joining two conformal field theories with possibly different central charge. Such defects can occur e. g. in the AdS/CFT correspondence when branes extend to the boundary of the AdS-space
2002
Article
http://edoc.mpg.de/3051
Journal of High Energy Physics, v.6 (2002)
en
oai:edoc.mpg.de:30542009-03-316:84
Perturbative Instabilities on the Non-Commutative Torus, Morita Duality and Twisted Boundary Conditions
Guralnik, Zachary
Helling, Robert C.
Landsteiner, Karl
Lopez, Esperanza
We study one-loop corrections in scalar and gauge field theories on the noncommutative torus. For rational theta, Morita equivalence allows these theories to be reformulated in terms of ordinary theories on a commutative torus with twisted boundary conditions . UV/IR mixing does not lead to singularities, however there can be large corrections. In particular, gauge theories show tachyonic instabilities for some of the modes. We discuss their relevance to spontaneous Z(N) x Z(N) symmetry breaking in the Morita dual SU(N) theory due to electric flux condensation
2002
Article
http://edoc.mpg.de/3054
Journal of High Energy Physics, v.6 (2002)
en
oai:edoc.mpg.de:30552009-03-316:84
Non-commutative gauge theory of twisted D-branes
Alekseev, Anton Yu.
Fredenhagen, Stefan
Quella, Thomas
Schomerus, Volker
In this work we propose new non-commutative gauge theories that describe the dynamics of branes localized along twisted conjugacy classes on group manifolds. Our proposal is based on a careful analysis of the exact microscopic solution and it generalizes the matrix models ("fuzzy gauge theories") that are used to study, e.g., the bound state formation of point-like branes in a curved background. We also construct a large number of classical solutions and interpret them in terms of condensation processes on branes localized along twisted conjugacy classes
2002
Article
http://edoc.mpg.de/3055
Nuclear Physics B, v.646, 127-157 (2002)
en
oai:edoc.mpg.de:30562009-03-316:84
Singular 7-manifolds with G(2) holonomy and intersecting 6-branes
Behrndt, Klaus
A 7-manifold with G(2) holonomy can be constructed as a R-3 bundle over a quaternionic space. We consider a quaternionic base space which is singular and its metric depends on three parameters, where one of them corresponds to an interpolation between S-4 and CP2 or its non-compact analogs. This 4d Einstein space has four isometrics and the fixed point set of a generic Killing vector is discussed. When embedded into M-theory the compactification over a given Killing vector gives intersecting 6-branes as IIA configuration and we argue that membrane instantons may resolve the curvature singularity
2002
Article
http://edoc.mpg.de/3056
Nuclear Physics B, v.635, 158-174 (2002)
en
oai:edoc.mpg.de:30672009-03-316:84
Monodromy of solutions of the Knizhnik-Zamolodchikov equation
Ponsot, Benedicte
Three explicit and equivalent representations for the monodromy of the conformal blocks in the SL(2,C)/SU(2) WZNW model are proposed in terms of the same quantity computed in Liouville field theory. We show that there are two possible fusion matrices in this model. This is due to the fact that the conformal blocks, being solutions to the Knizhnik-Zamolodchikov equation, have a singularity when the SL(2,C) isospin coordinate x equals the worldsheet variable z. We study the asymptotic behaviour of the conformal block when x goes to z. The obtained relation inserted into a four point correlation function in the SL(2,C)/SU(2) WZNW model gives some expression in terms of two correlation functions in Liouville field theory
2002
Article
http://edoc.mpg.de/3067
Nuclear Physics B, v.642, 114-138 (2002)
en
oai:edoc.mpg.de:30712009-03-316:84
Black hole entropy and thermodynamics from symmetries
Silva, Sebastian
Given a boundary of spacetime preserved by a Diff(S-1) sub-algebra, we propose a systematic method to compute the zero mode and the central extension of the associated Virasoro algebra of charges. Using these values in the Cardy formula, we may derive an associated statistical entropy to be compared with the Bekenstein-Hawking result. To illustrate our method, we study in detail the BTZ and the rotating, Kerr-adS(4) black holes (at spatial infinity and on the horizon). In both cases, we are able to reproduce the area law with the correct factor of 1/4 for the entropy. We also recover within our framework the first law of black-hole thermodynamics. We compare our results with the analogous derivations proposed by Carlip and others. Although similar, our method differs in the computation of the zero mode. In particular, the normalization of the ground state is automatically fixed by our construction
2002
Article
http://edoc.mpg.de/3071
Classical and Quantum Gravity, v.19, 3947-3961 (2002)
oai:edoc.mpg.de:30732009-03-306:84
Boundary RG-flows in coset conformal field theories
Fredenhagen, Stefan
Schomerus, Volker
We propose a new rule for boundary renormalization group flows in fixed-point free coset models. Our proposal generalizes the 'absorption of boundary spin'-principle formulated by Affleck and Ludwig to a large class of perturbations in boundary conformal field theories. We illustrate the rule in the case of unitary minimal models.
2003
Article
http://edoc.mpg.de/3073
Physical Review D, v.67 (2003)
en
oai:edoc.mpg.de:30742009-03-316:84
A New Double-Scaling Limit of N=4 Super Yang-Mills Theory and PP-Wave Strings
Kristjansen, Charlotte
Plefka, Jan
Semenoff, G.
Staudacher, Matthias
The metric of a spacetime with a parallel plane (pp)-wave can be obtained in a certain limit of the space AdS5 × S5 . According to the AdS/CFT correspondence, the holographic dual of superstring theory on that background should be the analogous limit of N=4 supersymmetric Yang?Mills theory. In this paper we shall show that, contrary to widespread expectation, non-planar diagrams survive this limiting procedure in the gauge theory. Using matrix model techniques as well as combinatorial reasoning it is demonstrated that a subset of diagrams of arbitrary genus survives and that a non-trivial double scaling limit may be defined. We exactly compute two- and three-point functions of chiral primaries in this limit. We also carefully study certain operators conjectured to correspond to string excitations on the pp-wave background. We find non-planar linear mixing of these proposed operators, requiring their redefinition. Finally, we show that the redefined operators receive non-planar corrections to the planar one-loop anomalous dimension
2002
Article
http://edoc.mpg.de/3074
Nuclear Physics B, v.643, 3-30 (2002)
en
oai:edoc.mpg.de:30782009-03-316:84
Conformal fields in the pp-wave limit
Arutyunov, Gleb
Sokatchev, E.
The pp-wave (Penrose limit) in a conformal field theory can be viewed as a special contraction of unitary representations of a conformal group. We study kinematics of conformal fields in the contraction limit by employing a geometric approach where the effect of the contraction can be visualized as an expansion of space-time. We discuss the two common models of space-time as carrier spaces for conformal fields: one is the usual Minkowski space and the other is a coset of the conformal group over its maximal compact subgroup. We show that only the latter manifold and the corresponding conformal representation theory admit a non-singular contraction limit. We also address a question about correlation functions of conformal fields in the pp-wave limit. We argue that finiteness of the (two-point) correlators under contraction can be achieved if their dependence on the coordinates of an R-symmetry group is kept on equal footing with their space-time dependence. This is a manifestation of the fact that in the contraction limit the space-time and R-symmetry groups become indistinguishable. Our results might find applications in actual calculations of correlation functions of composite operators in the ${cal N}=4$ super Yang-Mills theory
2002
Article
http://edoc.mpg.de/3078
Journal of High Energy Physics, v.8 (2002)
en
oai:edoc.mpg.de:30792009-03-316:84
Non-protected operators in N=4 SYM and multi-particle states of AdS_5 SUGRA
Arutyunov, Gleb
Penati, S.
Petkou, Anastasios C.
Santambrogio, A.
Sokatchev, E.
We study a class of non-protected local composite operators which emerge in the $SU(4)$-singlet channel of the OPE between two lowest dimension CPOs in ${cal N}=4$ SYM. These are quadrilinear operators which, in the free field limit, appear as double--trace color structures. When the interaction is turned on, a nontrivial mixing under renormalization occurs and they split in general into linear combinations of proper conformally invariant states which may involve both single and double traces. In a ${cal N}=1$ superspace setup we solve the mixing problem by computing the one-loop two point functions of all dimension 4 scalar operators, diagonalizing their anomalous dimension matrix and identifying the proper quasiprimary operators. We find one operator whose anomalous dimension is negative and suppressed by $1/N^2$ with respect to the anomalous dimensions of the Konishi--like operators. We identify the mechanism underlying such a suppression and give an argument to prove its occurrence at every order in perturbation theory. We discuss our results in connection with the AdS/CFT correspondence which requires such operators to be dual to multi-particle supergravity states whose energy is less than the sum of the corresponding individual single-particle states
2002
Article
http://edoc.mpg.de/3079
Nuclear Physics B, v.643, 49-78 (2002)
en
oai:edoc.mpg.de:30802009-03-316:84
Orientifolds and Ktheory
Braun, Volker
Stefanski, Bogdan
Recently it has been shown that D-branes in orientifolds are not always described by equivariant Real Ktheory. In this paper we define a previously unstudied twisted version of equivariant Real K-theory which gives the D-brane spectrum for such orientifolds. We find that equivariant Real K-theory can be twisted by elements of a generalised group cohomology. This cohomology classifies all orientifolds just as group cohomology classifies all orbifolds. As an example we consider the $Omega imesI_4$ orientifolds. We completely determine the equivariant orthogonal K-theory $KO_{Zop_2}(R^{p,q})$ and analyze the twisted versions. Agreement is found between K-theory and BCFT results for both integrally and torsion charged D-branes
2002
Other
http://edoc.mpg.de/3080
oai:edoc.mpg.de:30832009-03-306:84
Complexifier Coherent States for Quantum General Relativity
Thiemann, Thomas
Recently, substantial amount of activity in Quantum General Relativity (QGR) has focussed on the semiclassical analysis of the theory. In this paper we want to comment on two such developments: 1) Polymer-like states for Maxwell theory and linearized gravity constructed by Varadarajan which use much of the Hilbert space machinery that has proved useful in QGR and 2) coherent states for QGR, based on the general complexifier method, with built -- in semiclassical properties. We show the following: A) Varadarajans states {it are} complexifier coherent states. This unifies all states constructed so far under the general complexifier principle. B) Ashtekar and Lewandowski suggested a non-Abelean generalization of Varadarajans states to QGR which, however, are no longer of the complexifier type. We construct a new class of non-Abelean complexifiers which come close to the one underlying Varadarajans construction. C) Non-Abelean complexifiers close to Varadarajans induce new types of Hilbert spaces which do not support the operator algebra of QGR. The analysis suggests that if one sticks to the present kinematical framework of QGR and if kinematical coherent states are at all useful, then normalizable, graph dependent states must be used which are produced by the complexifier method as well. D) Present proposals for states with mildened graph dependence, obtained by performing a graph average, do not approximate well coordinate dependent observables. However, graph dependent states, whether averaged or not, seem to be well suited for the semiclassical analysis of QGR with respect to coordinate independent operator
2006
Article
http://edoc.mpg.de/3083
Classical and Quantum Gravity, v.23, 2063-2117 (2006)
en
oai:edoc.mpg.de:30852009-03-316:84
On the Spectrum of PP-Wave Matrix Theory
Kim, Nakwoo
Plefka, Jan
We study the spectrum of the recently proposed matrix model of DLCQ M-theory in a parallel plane (pp)-wave background. In contrast to matrix theory in a flat background this model contains mass terms, which lift the flat directions of the potential and renders its spectrum discrete. The supersymmetry algebra of the model groups the energy eigenstates into supermultiplets, whose members differ by fixed amounts of energy in great similarity to the representation of supersymmetry in AdS spaces. There is a unique and exact zero-energy groundstate along with a multitude of long and short multiplets of excited states. For large masses the quantum mechanical model may be treated perturbatively and we study the leading order energy shifts of the first excited states up to level two. Most interestingly we uncover a protected short multiplet at level two, whose energies do not receive perturbative corrections. Moreover, we conjecture the existence of an infinite series of similar protected multiplets in the pp-wave matrix model
2002
Article
http://edoc.mpg.de/3085
Nuclear Physics B, v.643, 31-48 (2002)
en
oai:edoc.mpg.de:30872009-03-306:84
Towards the QFT on Curved Spacetime Limit of QGR. 1: A General Scheme
Sahlmann, Hanno
Thiemann, Thomas
In this article and a companion paper we address the question of how one might obtain the semiclassical limit of ordinary matter quantum fields (QFT) propagating on curved spacetimes (CST) from full fledged Quantum General Relativity (QGR), starting from first principles. We stress that we do not claim to have a satisfactory answer to this question, rather our intention is to ignite a discussion by displaying the problems that have to be solved when carrying out such a program. In the present paper we propose a scheme that one might follow in order to arrive at such a limit. We discuss the technical and conceptual problems that arise in doing so and how they can be solved in principle. As to be expected, completely new issues arise due to the fact that QGR is a background independent theory. For instance, fundamentally the notion of a photon involves not only the Maxwell quantum field but also the metric operator - in a sense, there is no photon vacuum state but a "photon vacuum operator"! While in this first paper we focus on conceptual and abstract aspects, for instance the definition of (fundamental) n-particle states (e.g. photons), in the second paper we perform detailed calculations including, among other things, coherent state expectation values and propagation on random lattices. These calculations serve as an illustration of how far one can get with present mathematical techniques. Although they result in detailed predictions for the size of first quantum corrections such as the gamma-ray burst effect, these predictions should not be taken too seriously because a) the calculations are carried out at the kinematical level only and b) while we can classify the amount of freedom in our constructions, the analysis of the physical significance of possible choices has just begun
2006
Article
http://edoc.mpg.de/3087
Classical and Quantum Gravity, v.23, 867-908 (2006)
en
oai:edoc.mpg.de:30892009-03-306:84
Towards the QFT on Curved Spacetime Limit of QGR. 2: A Concrete Implementation
Sahlmann, Hanno
Thiemann, Thomas
The present paper is the companion of [1] in which we proposed a scheme that tries to derive the Quantum Field Theory (QFT) on Curved Spacetimes (CST) limit from background independent Quantum General Relativity (QGR). The constructions of [1] make heavy use of the notion of semiclassical states for QGR. In the present paper, we employ the complexifier coherent states for QGR recently proposed by Thiemann and Winkler as semiclassical states, and thus fill the general formulas obtained in [1] with life. We demonstrate how one can, under some simplifying assumptions, explicitely compute expectation values of the operators relevant for the gravity-matter Hamiltonians of [1] in the complexifier coherent states. These expectation values give rise to effective matter Hamiltonians on the background on which the gravitational coherent state is peaked and thus induce approximate notions of n-particle states and matter propagation on fluctuating spacetimes. We display the details for the scalar and the electromagnetic field. The effective theories exhibit two types of corrections as compared to the the ordinary QFT on CST. The first is due to the quantum fluctuations of the gravitational field, the second arises from the fact that background independence forces both geometry and matter to propagate on a spacetime that is the product of the real line and a (random) graph. Finally we obtain explicit numerical predictions for non-standard dispersion relations for the scalar and the electromagnetic field. They should, however, not be taken too seriously, due to the many ambiguities in our scheme, the analysis of the physical significance of which has only begun. We show however, that one can classify these ambiguities at least in broad terms
2006
Article
http://edoc.mpg.de/3089
Classical and Quantum Gravity, v.23, 909-954 (2006)
en
oai:edoc.mpg.de:30902009-03-316:84
Superalgebra for M-theory on a pp-wave
Kim, Nakwoo
Park, Jeong-Hyuck
We study the supersymmetry algebra of M-theory on a pp-wave. The algebra is identified as the special unitary Lie superalgebra, SU(2|4). The root structure is analysed. We discuss the typical and atypical representations and the atypicality conditions are derived by use of naturally ordered products. We also classify the BPS multiplets and find 1/4,1/2,3/4 and the fully supersymmetric representations are possible. Several examples are given with an emphasis on the properties of unitary representations.
2002
Article
http://edoc.mpg.de/3090
Physical Review D, v.66 (2002)
en
oai:edoc.mpg.de:30912009-03-316:84
Vacua of Maximal Gauged D=3 Supergravities
Fischbacher, Thomas
Nicolai, Hermann
Samtleben, Henning
We analyse the scalar potentials of maximal gauged three-dimensional supergravities which reveal a surprisingly rich structure. In contrast to maximal supergravities in dimensions D 4, all these theories possess a maximally supersymmetric (N = 16) ground state with negative cosmological constant < 0, except for the SO(4, 4)2 gauged theory, whose maximally supersymmetric groundstate has = 0. We compute the mass spectra of bosonic and fermionic fluctuations around these vacua and identify the unitary irreducible representations of the relevant background (super)isometry groups to which they belong. In addition, we find several stationary points which are not maximally supersymmetric, and determine their complete mass spectra as well. In particular, we show that there are analogues of all stationary points found in higher dimensions, among them are de Sitter (dS) vacua in the theories with noncompact gauge groups SO(5, 3)2 and SO(4,4)2, as well as anti-de Sitter (AdS) vacua in the compact gauged theory preserving 1/4 and 1/8 of the supersymmetries. All the dS vacua have tachyonic instabilities, whereas there do exist nonsupersymmetric AdS vacua which are stable, again in contrast to the D 4 theorie
2002
Article
http://edoc.mpg.de/3091
urn:ISSN:0264-9381
info:doi/10.1088/0264-9381/19/21/302
Classical and Quantum Gravity, v.19, 5297-5333 (2002)
en
oai:edoc.mpg.de:30952009-03-316:84
Some Comments on the Representation Theory of the Algebra Underlying Loop Quantum Gravity
Sahlmann, Hanno
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is singled out by its elegance and diffeomorphism covariance. Recently, in the context of the quest for semiclassical states, states of the theory in which the quantum gravitational field is close to some classical geometry, it was realized that it might also be worthwhile to study different representations of the algebra A of observables. The content of the present note is the observation that under some mild assumptions, the mathematical structure of representations of A can be analyzed rather effortlessly, to a certain extent: Each representation can be labeled by sets of functions and measures on the space of (generalized) connections that fulfill certain conditions. These considerations are however mostly of mathematical nature. Their physical content remains to be clarified, and physically interesting examples are yet to be constructed
2002
Other
http://edoc.mpg.de/3095
en
oai:edoc.mpg.de:30962009-03-316:84
When Do Measures on the Space of Connections Support the Triad Operators of Loop Quantum Gravity?
Sahlmann, Hanno
In this work we investigate the question, under what conditions Hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain non-Abelian analogues of the electric flux. We give the problem a precise mathematical formulation and start its investigation. For the technically simple case of U(1) as gauge group, we establish a number of ''no-go theorems'' asserting that for certain classes of measures, the flux operators can not be represented on the corresponding Hilbert spaces. The flux-observables we consider play an important role in loop quantum gravity since they can be defined without recurse to a background geometry, and they might also be of interest in the general context of quantization of non-Abelian gauge theories
2002
Other
http://edoc.mpg.de/3096
en
oai:edoc.mpg.de:30972009-03-316:84
Deformed Matrix Theories with N=8 and Fivebranes in the PP Wave Background
Kim, Nakwoo
Lee, Kimyeong M.
Yi, Piljin
M(atrix) theory is known to be mass-deformed in the pp-wave background and still retains all 16 dynamical supersymmetries. We consider generalization of such deformations on super Yang-Mills quantum mechanics (SYQM) with less supersymmetry. In particular this includes ${cal N}=8$ $U(N)$ SYQM with a single adjoint and any number of fundamental hypermultiplets, which is a pp-wave deformation of DLCQ matrix theory of fivebranes. With $kge 1$ fivebranes, we show that a rich vacuum structure exists, with many continuous family of solutions that preserve all dynamical supersymmetries. The vacuum moduli space contains disjoint copies of $CP^{k-1}$ of various sizes
2002
Article
http://edoc.mpg.de/3097
Journal of High Energy Physics, v.11 (2002)
en
oai:edoc.mpg.de:30982009-03-306:84
On Scherk-Schwarz mechanism in gauged five-dimensional supergravity and on its relation to bigravity
Lalak, Zygmunt
Matyszkiewicz, Radoslaw
We discuss flipped boundary conditions in five-dimensional brane worlds on S^1/Z_2 and the Scherk-Schwarz mechanism of supersymmetry breaking when some symmetries of the bulk supergravity coupled to mattter are gauged.
2003
Article
http://edoc.mpg.de/3098
Nuclear Physics B, v.649, 389-411 (2003)
en
oai:edoc.mpg.de:31002009-03-306:84
BMN Correlators and Operator Mixing in N=4 Super Yang-Mills Theory
Beisert, Niklas
Kristjansen, Charlotte
Plefka, Jan
Semenoff, G.
Staudacher, Matthias
Correlation functions in perturbative N=4 supersymmetric Yang-Mills theory are examined in the Berenstein-Maldacena-Nastase (BMN) limit. We demonstrate that non-extremal four-point functions of chiral primary fields are ill-defined in that limit. This lends support to the assertion that only gauge theoretic two-point functions should be compared to pp-wave strings. We further refine the analysis of the recently discovered non-planar corrections to the planar BMN limit. In particular, a full resolution to the genus one operator mixing problem is presented, leading to modifications in the map between BMN operators and string states. We give a perturbative construction of the correct operators and we identify their anomalous dimensions. We also distinguish symmetric, antisymmetric and singlet operators and find, interestingly, the same torus anomalous dimension for all three. Finally, it is discussed how operator mixing effects modify three point functions at the classical level and, at one loop, allow us to recover conformal invarianc
2003
Article
http://edoc.mpg.de/3100
Nuclear Physics B, v.650, 125-161 (2003)
en
oai:edoc.mpg.de:31042009-03-316:84
More comments on superstring interactions in the pp-wave background
Pankiewicz, Ari
We reconsider light-cone superstring field theory on the maximally supersymmetric pp-wave background. We find that the results for the fermionic Neumann matrices given so far in the literature are incorrect and verify our expressions by relating them to the bosonic Neumann matrices and proving several non-trivial consistency conditions among them, as for example the generalization of a flat space factorization theorem for the bosonic Neumann matrices. We also study the bosonic and fermionic constituents of the prefactor and point out a subtlety in the relation between continuum and oscillator basis expressions
2002
Article
http://edoc.mpg.de/3104
Journal of High Energy Physics, v.9 (2002)
en
oai:edoc.mpg.de:31052009-03-316:84
Introducing LambdaTensor 1.0 - A package for explicit symbolic and numeric Lie algebra and Lie group calculations
Fischbacher, Thomas
Due to the occurrence of large exceptional Lie groups in supergravity, calculations involving explicit Lie algebra and Lie group element manipulations easily become very complicated and hence also error-prone if done by hand. Research on the extremal structure of maximal gauged supergravity theories in various dimensions sparked the development of a library for efficient abstract multilinear algebra calculations involving sparse and non-sparse higher-rank tensors, which is presented here.
2002
Other
http://edoc.mpg.de/3105
en
oai:edoc.mpg.de:31092009-03-316:84
Are there really any AdS_2 branes in the euclidean (or not) AdS_3?
Ponsot, Benedicte
Silva, Sebastian
We do not find any AdS_2 branes, neither in the H_3^+ WZNW model nor the SL(2,R) WZNW model. We then reexamine the case of the branes that possess a su(2) symmetry: we speculate that they would have to live on the boundary of AdS_3. This cannot be realized in an euclidean spacetime, but in the SL(2,R) WZNW model by analytical continuation.
2002
Article
http://edoc.mpg.de/3109
Physics Letters B, v.551, 173-177 (2002)
en
oai:edoc.mpg.de:31122009-03-316:84
On the hierarchy of symmetry breaking D-branes in group manifolds
Quella, Thomas
We construct the boundary WZNW functional for symmetry breaking D-branes on a group manifold which are localized along a product of a number of twisted conjugacy classes and which preserve an action of an arbitrary continuous subgroup. These branes provide a geometric interpretation for the algebraic formulation of constructing D-branes developed recently in hep-th/0203161. We apply our results to obtain new symmetry breaking and non-factorizing D-branes in the background SL(2,R) x SU(2).
2002
Article
http://edoc.mpg.de/3112
Journal of High Energy Physics, v.12 (2002)
en
oai:edoc.mpg.de:31162009-03-316:84
Lectures on Branes in Curved Backgrounds
Schomerus, Volker
These lectures provide an introduction to the microscopic description of branes in curved backgrounds. After a brief reminder of the flat space theory, the basic principles and techniques of (rational) boundary conformal field theory are presented in the second lecture. The general formalism is then illustrated through a detailed discussion of branes on compact group manifolds. In the final lecture, many more recent developments are reviewed, inluding some results for non-compact target spaces.
2002
Article
http://edoc.mpg.de/3116
Classical and Quantum Gravity, v.19, 5781-5847 (2002)
en
oai:edoc.mpg.de:31172009-03-306:84
Low energy dynamics from deformed conformal symmetry in quantum 4D N=2 SCFTs
Kuzenko, Sergio M.
McArthur, I. N.
Theisen, Stefan
We determine the one-loop deformation of the conformal symmetry of a general N=2 superconformally invariant Yang-Mills theory. We compute the deformation for several explicit examples which have a realization as world-volume theories on a stack of D3 branes. This imposes restrictions on the effective action which we study on a subset of the Coulomb branch which corresponds to seperating one brane from the stack.
2003
Article
http://edoc.mpg.de/3117
urn:ISSN:0550-3213
info:doi/10.1016/S0550-3213(03)00231-1
Nuclear Physics B, v.660, 131-155 (2003)
en
oai:edoc.mpg.de:31252009-03-306:84
Topologizations of Chiral Representations
Conrady, Florian
Schweigert, Christoph
Recently, two different families of topologies have been proposed for representation spaces of chiral algebras. We prove a theorem that compares the two types of topologies and show that in one of them chiral blocks are continuous functionals.
2004
Article
http://edoc.mpg.de/3125
Communications in Mathematical Physics, v.245, 429-448 (2004)
en
oai:edoc.mpg.de:31262009-03-306:84
PP-Wave Light-Cone Superstring Field Theory
Pankiewicz, Ari
Stefanski, Bogdan
We construct the oscilator-basis expressions for the three-point vertex and dynamically generated supercharges in light-cone superstring field theory in the pp-wave background. We show that these satisfy the pp-wave superalgebra at first order in string coupling. Using this vertex we compute various string theory three-point functions and comment on their relation to gauge theory.
2003
Article
http://edoc.mpg.de/3126
Nuclear Physics B, v.657, 79-106 (2003)
en
oai:edoc.mpg.de:31272009-03-306:84
Lectures on Loop Quantum Gravity
Thiemann, Thomas
Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured over the past fifteen years to a mathematically rigorous candidate quantum field theory of the gravitational field. The features that distinguish it from other quantum gravity theories are 1) background independence and 2) minimality of structures. Background independence means that this is a non-perturbative approach in which one does not perturb around a given, distinguished, classical background metric, rather arbitrary fluctuations are allowed, thus precisely encoding the quantum version of Einsteins radical perception that gravity is geometry. Minimality here means that one explores the logical consequences of bringing together the two fundamental principles of modern physics, namely general covariance and quantum theory, without adding any experimentally unverified additional structures such as extra dimensions, extra symmetries or extra particle content beyond the standard model. While this is a very conservative approach and thus maybe not very attractive to many researchers, it has the advantage that pushing the theory to its logical frontiers will undoubtedly either result in a successful theory or derive exactly which extra structures are required, if necessary. Or put even more radically, it may show which basic principles of physics have to be given up and must be replaced by more fundamental ones. QGR therefore is, by definition, not a unified theory of all interactions in the standard sense since such a theory would require a new symmetry principle. However, it unifies all presently known interactions in a new sense by quantum mechanically implementing their common symmetry group, the four-dimensional diffeomorphism group, which is almost completely broken in perturbative approaches
Springer
2003
InBook
http://edoc.mpg.de/3127
Quantum Gravity: From Theory to Experimental Search, 41-135 (2003)
en
oai:edoc.mpg.de:31282009-03-306:84
Supersymmetry and Branes in M-theory Plane-Waves
Kim, Nakwoo
Yee, Jung-Tay
We study brane embeddings in M-theory plane-waves and their supersymmetry. The relation with branes in AdS backgrounds via the Penrose limit is also explored. Longitudinal planar branes are originated from AdS branes while giant gravitons of AdS spaces become spherical branes which are realized as fuzzy spheres in the massive matrix theory.
2003
Article
http://edoc.mpg.de/3128
Physical Review D, v.67 (2003)
en
oai:edoc.mpg.de:31292009-03-306:84
BMN Operators and Superconformal Symmetry
Beisert, Niklas
Implications of N=4 superconformal symmetry on Berenstein-Maldacena-Nastase (BMN) operators with two charge defects are studied both at finite charge J and in the BMN limit. We find that all of these belong to a single long supermultiplet explaining a recently discovered degeneracy of anomalous dimensions on the sphere and torus. The lowest dimensional component is an operator of naive dimension J+2 transforming in the [0,J,0] representation of SU(4). We thus find that the BMN operators are large J generalisations of the Konishi operator at J=0. We explicitly construct descendant operators by supersymmetry transformations and investigate their three-point functions using superconformal symmet
2003
Article
http://edoc.mpg.de/3129
Nuclear Physics B, v.659, 79-118 (2003)
en
oai:edoc.mpg.de:31302009-03-306:84
Gravitational corrections in supersymmetric gauge theory and matrix models
Klemm, Albrecht
Marino, Marcus
Theisen, Stefan
Gravitational corrections in N=1 and N=2 supersymmetric gauge theories are obtained from topological string amplitudes. We show how they are recovered in matrix model computations. This provides a test of the proposal by Dijkgraaf and Vafa beyond the planar limit. Both, matrix model and topological string theory, are used to check a conjecture of Nekrasov concerning these gravitational couplings in Seiberg-Witten theory. Our analysis is performed for those gauge theories which are related to the cubic matrix model, i.e. pure SU(2) Seiberg-Witten theory and N=2 U(N) SYM broken to N=1 via a cubic superpotential. We outline the computation of the topological amplitudes for the local Calabi-Yau manifolds which are relevant for these two ca
2003
Article
http://edoc.mpg.de/3130
urn:ISSN:1029-8479
info:doi/10.1088/1126-6708/2003/03/051
Journal of High Energy Physics, v.03 (2003)
en
oai:edoc.mpg.de:31312009-03-306:84
Asymmetric Cosets
Quella, Thomas
Schomerus, Volker
The aim of this work is to present a general theory of coset models G/H in which different left and right actions of H on G are gauged. Our main results include a formula for their modular invariant partition function, the construction of a large set of boundary states and a general description of the corresponding brane geometries. The paper concludes with some explicit applications to the base of the conifold and to the time-dependent Nappi-Witten background.
2003
Article
http://edoc.mpg.de/3131
Journal of High Energy Physics, v.2 (2003)
en
oai:edoc.mpg.de:31322009-03-306:84
Cosmological Billiards
Damour, Thibault
Henneaux, Marc
Nicolai, Hermann
It is shown in detail that the dynamics of the Einstein-dilaton-p-form system in the vicinity of a spacelike singularity can be asymptotically described, at a generic spatial point, as a billiard motion in a region of Lobachevskii space (realized as an hyperboloid in the space of logarithmic scale factors). This is done within the Hamiltonian formalism, and for an arbitrary number of spacetime dimensions $D geq 4$. A key role in the derivation is played by the Iwasawa decomposition of the spatial metric, and by the fact that the off-diagonal degrees of freedom, as well as the p-form degrees of freedom, get ''''asymptotically frozen'' in this description. For those models admitting a Kac-Moody theoretic interpretation of the billiard dynamics we outline how to set up an asymptotically equivalent description in terms of a one-dimensional non-linear sigma-model formally invariant under the corresponding Kac-Moody grou
2003
Article
http://edoc.mpg.de/3132
urn:ISSN:0264-9381
info:doi/10.1088/0264-9381/20/9/201
Classical and Quantum Gravity, v.20, R145-R200 (2003)
en
oai:edoc.mpg.de:31362009-03-306:84
Correlation functions and massive Kaluza-Klein modes in the AdS/CFT correspondence
Arutyunov, Gleb
Dolan, F. A.
Osborn, H.
Sokatchev, E.
We study four-point correlation functions of 1/2-BPS operators in N=4 SYM which are dual to massive KK modes in AdS_5 supergravity. On the field theory side, the procedure of inserting the SYM action yields partial non-renormalisation of the four-point amplitude for such operators. In particular, if the BPS operators have dimensions equal to three or four, the corresponding four-point amplitude is determined by one or two independent functions of the two conformal cross-ratios, respectively. This restriction on the amplitude does not merely follow from the superconformal Ward identities, it also encodes dynamical information related to the structure of the gauge theory Lagrangian. The dimension 3 BPS operator is the AdS/CFT dual of the first non-trivial massive Kaluza-Klein mode of the compactified type IIB supergravity, whose interactions go beyond the level of the five-dimensional gauged N=8 supergravity. We show that the corresponding effective Lagrangian has a surprisingly simple sigma-model-type form with at most two derivatives. We then compute the supergravity-induced four-point amplitude for the dimension 3 operators. Remarkably, this amplitude splits into a "free" and an "interacting" parts in exact agreement with the structure predicted by the insertion procedure. The underlying OPE fulfills the requirements of superconformal symmetry and unitarity.
2003
Article
http://edoc.mpg.de/3136
Nuclear Physics B, v.665, 273-324 (2003)
en
oai:edoc.mpg.de:31372009-03-306:84
Remarks on IIB pp-waves with Ramond-Ramond fluxes and massive two dimensional nonlinear sigma models
Kim, Nakwoo
We continue the study of supersymmetric IIB pp-wave solutions by Maldacena and Maoz (hep-th/0207284), who showed Ramond-Ramond five-forms can induce potential terms in the light cone string actions which are nonlinear sigma models with special holonomy target spaces. We show nonvanishing Ramond-Ramond three-forms provide extra potential terms involving Killing vectors in the string action and identify the supersymmetry requirements. In particular, in solutions with $(1,1)$ worldsheet supersymmetry, the Killing vectors are required to be self-dual in Spin(7
2003
Article
http://edoc.mpg.de/3137
Physical Review D, v.67 (2003)
en
oai:edoc.mpg.de:31742009-03-306:84
Instanton-induced Yang-Mills correlation functions at large N and their AdS5 x S5 duals
Green, Michael B.
Kovacs, Stefano
Correlation functions of chiral primary operators and their superconformal descendants in the N=4 supersymmetric SU(N) Yang-Mills theory are studied in detail in a one-instanton background and at large N. Whereas earlier calculations were restricted to correlation functions that are saturated by the 16 exact superconformal fermionic moduli, here the effect of the infinite set of additional fermionic moduli associated with the embeddings of the SU(2) instanton in SU(N) is considered. The presence of the extra fermionic modes is essential for matching Yang-Mills instanton effects in various correlation functions with D-instanton effects in type IIB string theory via the AdS/CFT conjecture. The leading terms of this kind on the string side contribute at order $\alpha^{-1}$ (where the Einstein--Hilbert terms are of order $\alpha^{-4}$), which is the same order as the $R^4$ interaction. For example, the instanton contributions to correlation functions of higher dimensional chiral primary operators are seen to match amplitudes involving Kaluza-Klein excitations of the supergravity fields, as expected. Another example is the matching of certain multi-fermion correlation functions which correspond to certain multi-fermion interactions required by supersymmetry of the IIB string effective action. Careful analysis of a variety of competing effects makes it possible to decipher contributions corresponding to higher derivative interactions in the IIB effective action. In this manner it is possible to check for the presence of terms of order \alpha$. Comments are also made on the structure of instanton contributions to near-extremal correlation functions of chiral primary operator
2003
Article
http://edoc.mpg.de/3174
Journal of High Energy Physics, v.04 (2003)
en
oai:edoc.mpg.de:31752009-03-306:84
BMN Gauge Theory as a Quantum Mechanical System
Beisert, Niklas
Kristjansen, Charlotte
Plefka, Jan
Staudacher, Matthias
We derive an effective, exact quantum mechanical Hamiltonian from N=4 gauge theory in the BMN limit. Its eigenvalues yield the one-loop anomalous dimensions of scalar two-impurity BMN operators for all genera. It is demonstrated that this reformulation vastly simplifies computations. E.g.~the known anomalous dimension formula for genus one is reproduced through a one-line calculation. We also efficiently evaluate the genus two correction, finding a non-vanishing result. We comment on multi-trace two-impurity operators and we conjecture that our quantum-mechanical reformulation could be extended to higher quantum loops and more impurities
2003
Article
http://edoc.mpg.de/3175
Physics Letters B, v.558, 229-237 (2003)
en
oai:edoc.mpg.de:31822009-03-316:84
Open Strings and Non-commutative Geometry of Branes on Group Manifolds
Alekseev, Anton Yu.
Recknagel, Andreas
Schomerus, Volker
In this contribution we review some recent work on the non-commutative geometry of branes on group manifolds. In particular, we show how fuzzy spaces arise in this context from an exact world-sheet description and we sketch the construction of a low-energy effective action for massless open string modes. The latter is given by a combination of a Yang-Mills and a Chern-Simons like functional on the fuzzy world-volume. It can be used to study condensation on various brane configurations in curved backgrounds.
2001
Article
http://edoc.mpg.de/3182
Modern Physics Letters A, v.16, 325-336 (2001)
en
oai:edoc.mpg.de:32012009-04-026:84
Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results
Ambjörn, Jan
Jurkiewicz, Jerzy
Loll, Renate
We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual space-time geometries are constructed from fundamental simplicial building blocks, and the path integral over geometries is approximated by summing over a class of piece-wise linear geometries. This method of ''''dynamical triangulations'' is very powerful in 2d, where the regularized theory can be solved explicitly, and gives us more insights into the quantum nature of 2d space-time than continuum methods are presently able to provide. It also allows us to establish an explicit relation between the Lorentzian-and Euclidean-signature quantum theories. Analogous regularized gravitational models can be set up in higher dimensions. Some analytic tools exist to study their state sums, but, unlike in 2d, no complete analytic solutions have yet been constructed. However, a great advantage of our approach is the fact that it is well-suited for numerical simulations. In the second part of this review we describe the relevant Monte Carlo techniques, as well as some of the physical results that have been obtained from the simulations of Euclidean gravity. We also explain why the Lorentzian version of dynamical triangulations is a promising candidate for a non-perturbative theory of quantum gravity
2000
InBook
http://edoc.mpg.de/3201
M-Theory and Quantum Geometry: Proceedings of the NATO Advanced Study Institute, 382-449 (2000)
en
oai:edoc.mpg.de:32022009-04-026:84
The Asymptotic Groundstate of SU(3) Matrix Theory
Hoppe, Jens
Plefka, Jan
The asymptotic form of a SU(3) matrix theory groundstate is found by showing that a recent ansatz for a supersymmetric wavefunction is non-trivial (i.e. non-zero).
2000
Other
http://edoc.mpg.de/3202
en
oai:edoc.mpg.de:32092009-04-026:84
Holographic Duality, Supersymmetry, and Painleve Equation
Ketov, Sergei V.
2000
Other
http://edoc.mpg.de/3209
en
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