Abstract
We construct the supersymmetric completion of E6(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 SO(1, 4) × USp(8) and transform as weighted scalars under the E6(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.