Exceptional Field Theory for $E_{6(6)}$ supergravity

A brief description of the supersymmetric and duality covariant approach to supergravity is presented. The formalism is based on exceptional geometric structures and turns the hidden U-duality group into a manifest gauge symmetry. Tensor hierarchy of gauged supergravity appears naturally here as a consequence of covariance of the construction. Finally, the full supersymmetric Lagrangian is explicitly constructed. This work was presented on the International Conference “Quantum Field Theory and Gravity (QFTG’14)” in Tomsk.