Fermionic Kac-Moody Billiards and Supergravity

Abstract

We study the "fermionic billiards", i.e. the chaotic dynamics of the gravitino, that arise in the near-spacelike-singularity limit of eleven-dimensional supergravity and of its dimensional truncations (notably four-dimensional simple supergravity). By exploiting the gravity-coset correspondence, we show that the billiard dynamics of the gravitino is described by a `spin extension' of the E(10) Weyl group, namely as a product of 90 degree `vector-spinor rotations' along certain simple-root-related generators of the maximal compact subalgebra K(E(10)) of the hyperbolic Kac--Moody algebra E(10). The `super-billiard' that combines the bosonic and fermionic billiards is found to have a remarkably simple structure, which exhibits a striking analogy with a polarized photon propagating in the ten-dimensional Lorentzian Weyl chamber of E(10).

55 pages

References in corpus (6)

• Spacelike Singularities and Hidden Symmetries of Gravity
• Hidden symmetries and the fermionic sector of eleven-dimensional supergravity
• Extended E8 Invariance of 11-Dimensional Supergravity
• K(E10), Supergravity and Fermions
• Describing general cosmological singularities in Iwasawa variables
• Constraints and the E10 Coset Model

Cited by in corpus (11)

• Quantum Supersymmetric Bianchi IX Cosmology
• On higher spin realizations of K(E10)
• Quantum Einstein-Dirac Bianchi Universes
• Mathematical General Relativity
• Representations of involutory subalgebras of affine Kac-Moody algebras
• Canonical structure of the E10 model and supersymmetry
• Quantum Supersymmetric Cosmological Billiards and their Hidden Kac-Moody Structure
• A Lightcone Embedding of the Twin Building of a Hyperbolic Kac-Moody Group
• Generalised holonomies and K(E${}_9$)
• $\pi$-systems and the embedding problem for rank $2$ Kac-Moody Lie algebras
• Hidden Kac-Moody Structures in the Fermionic Sector of Five-Dimensional Supergravity