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          Institute: MPI für Gravitationsphysik     Collection: Quantum Gravity and Unified Theories     Display Documents

ID: 119227.0, MPI für Gravitationsphysik / Quantum Gravity and Unified Theories
On KE(9)
Authors:Nicolai, Hermann; Samtleben, Henning
Date of Publication (YYYY-MM-DD):2005
Title of Journal:Quarterly Journal of Pure and Applied Mathematics
Start Page:180
End Page:204
Review Status:not specified
Audience:Not Specified
Abstract / Description:We study the maximal compact subgroup K(E_9) of the affine Lie group E_9(9) and its on-shell realization as an R symmetry of maximal N=16 supergravity in two dimensions. We first give a rigorous definition of the group K(E_9), which lives on the double cover of the spectral parameter plane, and show that the infinitesimal action of K(E_9) on the chiral components of the bosons and the fermions is determined in terms of an expansion of the Lie algebra of K(E_9) about the two branch points of this cover; this implies in particular that the fermions of N=16 supergravity transform in a spinor representation of K(E_9). The fermionic equations of motion can be fitted into the lowest components of a single K(E_9) covariant `Dirac equation', with the linear system of N=16 supergravity as the gauge connection. These results suggest the existence of an `off-shell' realization of K(E_9) in terms of an infinite component spinor representation. We conclude with some coments on `generalized holonomies' of M theory.
External Publication Status:published
Document Type:Article
Communicated by:Hermann Nicolai
Affiliations:MPI für Gravitationsphysik/Quantum Gravity and Unified Theories
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