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

Understand

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.