A master exceptional field theory

TL;DR

This paper constructs an $E_{11}$-invariant pseudo-Lagrangian that unifies various exceptional field theories and reproduces eleven-dimensional supergravity, offering a framework for maximal supersymmetry and higher dual fields.

Contribution

It introduces a new $E_{11}$-invariant pseudo-Lagrangian that encompasses all maximal supergravity theories and includes higher dual fields like the dual graviton.

Findings

Reduces to 11D supergravity for specific section condition

Reproduces $E_8$ exceptional field theory with alternative section

Suggests a unified framework for all maximal supergravities

Abstract

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. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the $E_{10}$ sigma model.