On supersymmetric E11 exceptional field theory

We construct an infinite system of non-linear duality equations, including fermions, that are invariant under global E-11 and gauge invariant under generalised diffeomorphisms upon the imposition of a suitable section constraint. We use finite-dimensional fermionic representations of the R-symmetry K(E-11) to describe the fermionic contributions to the duality equations. These duality equations reduce to the known equations of E-8 exceptional field theory or eleven-dimensional supergravity for appropriate (partial) solutions of the section constraint. Of key importance in the construction is an indecomposable representation of E-11 that entails extra non-dynamical fields beyond those predicted by E-11 alone, generalising the known constrained p-forms of exceptional field theories. The construction hinges on the tensor hierarchy algebra extension of e11, both for the bosonic theory and its supersymmetric extension.