Exceptional Lie algebras and M-theory

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.

PhD thesis, defended on December 10, 2008

References in corpus (6)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• On the structure of k-Lie algebras
• E10 and Gauged Maximal Supergravity
• Generalized conformal realizations of Kac-Moody algebras

Cited by in corpus (2)

• Arithmetic and Hyperbolic Structures in String Theory
• Generalized spin representations