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 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 \( {\mathfrak{e}}_{11} \), both for the bosonic theory and its supersymmetric extension.
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Bossard, G., Kleinschmidt, A. & Sezgin, E. On supersymmetric E11 exceptional field theory. J. High Energ. Phys. 2019, 165 (2019). https://doi.org/10.1007/JHEP10(2019)165
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DOI: https://doi.org/10.1007/JHEP10(2019)165