A master exceptional field theory

Understand

We construct a pseudo-Lagrangian that is invariant under rigid $E_{11}$ and transforms as a density under $E_{11}$ generalised diffeomorphisms.

• The gauge-invariance requires the use of a section condition studied in previous work on $E_{11}$ exceptional field theory and the inclusion of constrained fields that transform in an indecomposable $E_{11}$-representation together with the $E_{11}$ coset fields.
• We show that, in combination with gauge-invariant and $E_{11}$-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condition.
• For another choice, we reobtain the $E_8$ exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension.