Exceptional Lie algebras and M-theory

Details Exceptional Lie algebras and M-theory Exceptional Lie algebras and M-theory

2009-12-08

arxiv.org/abs/0912.1612v1

Physics

High Energy Physics

High Energy Physics - Theory

PhD thesis, defended on December 10, 2008

Scientific paper

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.

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