Exceptional Lie algebras and M-theory

TL;DR

This thesis explores the role of exceptional Lie algebras, especially e8, e9, and e10, in M-theory, highlighting their algebraic structures and connections to supergravity and brane theories.

Contribution

It provides a detailed analysis of the algebraic structures underlying M-theory, including the graded Lie algebra e10 and its relation to supergravity and brane models.

Findings

E10 as a graded Lie algebra is key to supergravity equivalence.

Generalized Jordan triple systems relate to graded Lie algebras and M2-brane descriptions.

The thesis reviews the dynamical equivalence between supergravity and sigma models based on E10.

Abstract

In this thesis we study algebraic structures in M-theory, in particular the exceptional Lie algebras arising in dimensional reduction of its low energy limit, eleven-dimensional supergravity. We focus on e8 and its infinite-dimensional extensions e9 and e10. We review the dynamical equivalence, up to truncations on both sides, between eleven-dimensional supergravity and a geodesic sigma model based on the coset E10/K(E10), where K(E10) is the maximal compact subgroup. The description of e10 as a graded Lie algebra is crucial for this equivalence. We study generalized Jordan triple systems, which are closely related to graded Lie algebras, and which may also play a role in the description of M2-branes using three-dimensional superconformal theories.