A master exceptional field theory

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.

Minor corrections, accepted for publication in JHEP

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• Teleparallelism in the algebraic approach to extended geometry
• The E10 Wheeler-DeWitt operator at low levels
• Extended geometry of magical supergravities
• Type II Double Field Theory in Superspace
• Higher dualisations of linearised gravity and the $A_1^{+++}$ algebra
• The teleparallel complex
• Unfolding $E_{11}$
• Infinite affine, hyperbolic and Lorentzian Weyl groups with their associated Calogero models
• The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces
• A Calogero Model with root string representatives of infinite order Coxeter orbits