# On supersymmetric E11 exceptional field theory

## TL;DR

This paper develops an infinite set of non-linear duality equations invariant under E11, incorporating fermions and extending exceptional field theory to include supersymmetry and additional non-dynamical fields.

## Contribution

It introduces a supersymmetric extension of E11 exceptional field theory using tensor hierarchy algebra, including fermions and extra non-dynamical fields beyond standard predictions.

## Key findings

- Reduces to known E8 exceptional field theory equations under certain conditions
- Incorporates fermionic contributions using finite-dimensional E11 representations
- Extends the tensor hierarchy algebra to include supersymmetric and non-dynamical fields

## Abstract

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 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.