On supersymmetric E ₁₁ exceptional field theory

We construct an infinite system of non-linear duality equations, including fermions, that are invariant under global E₁₁ 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(E₁₁) to describe the fermionic contributions to the duality equations. These duality equations reduce to the known equations of E₈ 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 E₁₁ that entails extra non-dynamical fields beyond those predicted by E₁₁ 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.