The gauge structure of Exceptional Field Theories and the tensor hierarchy

Understand

We address the construction of manifest U-duality invariant generalized diffeomorphisms.

• The closure of the algebra requires an extension of the tangent space to include a tensor hierarchy indicating the existence of an underlying unifying structure, compatible with E_{11} and Borcherds algebras constructions.
• We begin with four-dimensional gauged maximal supergravity, and build a generalized Lie derivative that encodes all the gauge transformations of the theory.
• A generalized frame is introduced, which accommodates for all the degrees of freedom, including the tensor hierarchy.