We give the supersymmetric extension of exceptional field theory for
E7(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)×SU(8) and transform as scalar
densities under the E7(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.Comment: 38 pages + appendices; published version (JHEP