Fermionic Kac-Moody Billiards and Supergravity

TL;DR

This paper explores the chaotic dynamics of the gravitino in eleven-dimensional supergravity near singularities, revealing a spin-extended E(10) symmetry that combines bosonic and fermionic billiard behaviors.

Contribution

It introduces a novel description of fermionic billiards using a spin extension of the E(10) Weyl group, linking supergravity dynamics to hyperbolic Kac--Moody algebra structures.

Findings

Fermionic billiards are governed by a spin extension of E(10) Weyl group.

The super-billiard exhibits a simple structure analogous to photon propagation.

The dynamics unify bosonic and fermionic behaviors in a common geometric framework.

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).