Fermions and Supersymmetry in $\rm E_{6(6)}$ Exceptional Field Theory

TL;DR

This paper develops a supersymmetric extension of E6(6) exceptional field theory, unifying 11D supergravity and IIB supergravity within a covariant framework using a 5+27-dimensional space-time.

Contribution

It constructs the complete supersymmetric Lagrangian for E6(6) exceptional field theory, including fermions and their transformations, and demonstrates its invariance under supersymmetry.

Findings

The theory embeds 11D supergravity and IIB supergravity solutions.

The Lagrangian is explicitly constructed and shown to be supersymmetry invariant.

Fermions are tensors under local Lorentz and transform as scalars under generalized diffeomorphisms.

Abstract

We construct the supersymmetric completion of E$_{6(6)}$-covariant exceptional field theory. The theory is based on a $(5+27)$-dimensional generalized space-time subject to a covariant section constraint. The fermions are tensors under the local Lorentz group ${\rm SO}(1,4)\times {\rm USp}(8)$ and transform as weighted scalars under the E$_{6(6)}$ (internal) generalized diffeomorphisms. We present the complete Lagrangian and prove its invariance under supersymmetry. Upon explicit solution of the section constraint the theory embeds full $D=11$ supergravity and IIB supergravity, respectively.