E10 and a "small tension expansion" of M Theory

TL;DR

This paper demonstrates that a small tension expansion of D=11 supergravity near a spacelike singularity corresponds to a null geodesic motion in the infinite-dimensional coset space E10/K(E10), revealing a deep algebraic structure underlying supergravity.

Contribution

It establishes a detailed correspondence between supergravity near singularities and geodesic motion in E10, using a novel decomposition of E10 into SL(10,R) representations.

Findings

Equivalence up to 30th order in the tension expansion.

Identification of the first four E10 coset fields with supergravity quantities.

Explicit decomposition of E10 into irreducible SL(10,R) representations.

Abstract

A formal ``small tension'' expansion of D=11 supergravity near a spacelike singularity is shown to be equivalent, at least up to 30th order in height, to a null geodesic motion in the infinite dimensional coset space E10/K(E10) where K(E10) is the maximal compact subgroup of the hyperbolic Kac-Moody group E10(R). For the proof we make use of a novel decomposition of E10 into irreducible representations of its SL(10,R) subgroup. We explicitly show how to identify the first four rungs of the E10 coset fields with the values of geometric quantities constructed from D=11 supergravity fields and their spatial gradients taken at some comoving spatial point.