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ID: 341855.0, MPI für Gravitationsphysik / Quantum Gravity and Unified Theories
Conformal internal symmetry of 2d σ-models coupled to gravity and a dilaton
Authors:Julia, Bernard; Nicolai, Hermann
Date of Publication (YYYY-MM-DD):1996-12
Title of Journal:Nuclear Physics B
Issue / Number:1-2
Start Page:431
End Page:465
Review Status:not specified
Audience:Not Specified
Abstract / Description:General relativity reduced to two dimensions possesses a large group of symmetries that exchange classical solutions. The associated Lie algebra is known to contain the affine Kac-Moody algebra A1(1) and half of a real Witt algebra. In this paper we exhibit the full symmetry under the semi-direct product of Lie A(1(1)) by the Witt algebra Lie (Image), Furthermore we exhibit the corresponding hidden gauge symmetries. We show that the theory can be understood in terms of an infinite dimensional potential space involving all degrees of freedom: the dilaton as well as matter and gravitation. In the dilaton sector the linear system that extends the previously known Lax pair has the form of a twisted self-duality constraint that is the analog of the self-duality constraint arising in extended supergravities in higher space-time dimensions. Our results furnish a group theoretical explanation for the simultaneous occurrence of two spectral parameters, a constant one (= y) and a variable one (= t). They hodl for all 2d non-linear σ-models that are obtained by dimensional reduction of G/H models in three dimensions coupled to pure gravity. In that case the Lie algebra is Lie (Imagetimes sign, left closed G(1)); this symmetry acts on a set of off-shell fields (in a fixed gauge) and preserves the equations of motion.
External Publication Status:published
Document Type:Article
Communicated by:Hermann Nicolai
Affiliations:MPI für Gravitationsphysik/Quantum Gravity and Unified Theories
External Affiliations:Institute for Theoretical Physics, Hamburg University Luruper Chaussee 149, 22761 Hamburg, Germany
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