Séminaire de Physique Théorique

On Supersymmetric E11 Exceptional Field Theory

by Prof. Guillaume Bossard (Centre de Physique Théorique, CNRS, Ecole Polytechnique, IP Paris)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane

IHES

35, route de Chartres, F-91440 Bures-sur-Yvette (France)
Description

We shall review how supergravity theories can emerge from an exceptional field theory based on the Kac-Moody group E11 (i.e. E8+++) with gauge symmetry a set of `generalised diffeomorphisms' acting on the fundamental module while preserving E11. The construction relies on a super-algebra T  that extends E11 and provides a differential complex for the exceptional fields. A twisted self-duality equation underlying the dynamics can be shown to be invariant under generalised diffeomorphisms provided a certain algebraic identity holds for structure coefficients of the super-algebra T. The fermions of the theory belong to an unfaithful representation of the double cover of a maximal Lorentzian subgroup K(E11). We conjecture that certain tensor products of unfaithful representations are homomorphic to the quotient of specific indecomposable modules of E11. Using these conjectures, we can write a linearised Rarita-Schwinger equation and show that the E11 twisted self-duality equations are supercovariant. The conjectures are checked through computations in level decompositions with respect to maximal parabolic subgroups.

Organized by

Thibault Damour

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