On supersymmetric E11 exceptional field theory

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.

90 pages. v2: Minor corrections, new references and new section 4.3 on linearised duality equations, JHEP version. v3: Minor corrections

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Cited by in corpus (20)

• A master exceptional field theory
• E${}_9$ exceptional field theory II. The complete dynamics
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• Beyond the standard model with six-dimensional spinors
• Tensor hierarchy algebras and extended geometry I: Construction of the algebra
• Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras
• On symmetries and dynamics of exotic supermultiplets
• Exploring the geometry of supersymmetric double field theory
• Generalized Dualities and Supergroups
• Maximal D=2 supergravities from higher dimensions
• Teleparallelism in the algebraic approach to extended geometry
• The E10 Wheeler-DeWitt operator at low levels
• Type II Double Field Theory in Superspace
• Extended geometry of magical supergravities
• The teleparallel complex
• Generalised holonomies and K(E${}_9$)
• Unfolding $E_{11}$
• Exotic branes and mixed-symmetry potentials II: Duality rules and exceptional $p$-form gauge fields
• The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces
• Localized Kaluza-Klein 6-brane