Supersymmetric E7(7) exceptional field theory

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 SO(1, 3) x 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.