Supersymmetric E$_{7(7)}$ Exceptional Field Theory

TL;DR

This paper develops a supersymmetric extension of E7(7) exceptional field theory, integrating fermions and supersymmetry transformations into a covariant framework consistent with 11-dimensional supergravity.

Contribution

It introduces the supersymmetric extension of E7(7) exceptional field theory with manifest covariance and demonstrates its consistency with 11D supergravity.

Findings

Supersymmetry transformations close into generalized diffeomorphisms.

Fermionic field equations are derived and shown to be supersymmetry invariant.

The framework is consistent with generalized geometric formulations of 11D supergravity.

Abstract

We give the supersymmetric extension of exceptional field theory for E$_{7(7)}$, which is based on a $(4+56)$-dimensional generalized spacetime subject to a covariant constraint. The fermions are tensors under the local Lorentz group ${\rm SO}(1,3)\times {\rm SU}(8)$ and transform as scalar densities under the E$_{7(7)}$ (internal) generalized diffeomorphisms. The supersymmetry transformations are manifestly covariant under these symmetries and close, in particular, into the generalized diffeomorphisms of the 56-dimensional space. We give the fermionic field equations and prove supersymmetric invariance. We establish the consistency of these results with the recently constructed generalized geometric formulation of $D=11$ supergravity.