Extended E8 Invariance of 11-Dimensional Supergravity

TL;DR

This paper explores the extension of E8 symmetry in 11-dimensional supergravity, demonstrating that the symmetry structure persists when including gravitino fields, thus deepening the understanding of supergravity's underlying algebraic framework.

Contribution

It extends previous work by showing that E8 invariance in supergravity remains valid when gravitino fields are incorporated, not just at the bosonic level.

Findings

E8 symmetry extends to include gravitino fields

Supergravity equations can be reformulated as a non-linear sigma model

Symmetry structures are consistent with previous bosonic level results

Abstract

The hyperbolic Kac-Moody algebra E10 has repeatedly been suggested to play a crucial role in the symmetry structure of M-theory. Recently, following the analysis of the asymptotic behaviour of the supergravity fields near a cosmological singularity, this question has received a new impulse. It has been argued that one way to exhibit the symmetry was to rewrite the supergravity equations as the equations of motion of the non-linear sigma model E10/K(E10). This attempt, in line with the established result that the scalar fields which appear in the toroidal compactification down to three spacetime dimensions form the coset E8/SO(16), was verified for the first bosonic levels in a level expansion of the theory. We show that the same features remain valid when one includes the gravitino field