Beyond E11

Abstract

We study the non-linear realisation of E11 originally proposed by West with particular emphasis on the issue of linearised gauge invariance. Our analysis shows even at low levels that the conjectured equations can only be invariant under local gauge transformations if a certain section condition that has appeared in a different context in the E11 literature is satisfied. This section condition also generalises the one known from exceptional field theory. Even with the section condition, the E11 duality equation for gravity is known to miss the trace component of the spin connection. We propose an extended scheme based on an infinite-dimensional Lie superalgebra, called the tensor hierarchy algebra, that incorporates the section condition and resolves the above issue. The tensor hierarchy algebra defines a generalised differential complex, which provides a systematic description of gauge invariance and Bianchi identities. It furthermore provides an E11 representation for the field strengths, for which we define a twisted first order self-duality equation underlying the dynamics.

97 pages. v2: Minor changes, references added. Published version

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• Kac-Moody Spectrum of (Half-)Maximal Supergravities
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• Forms and algebras in (half-)maximal supergravity theories
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Cited by in corpus (30)

• The Geometry, Branes and Applications of Exceptional Field Theory
• Generalised diffeomorphisms for E${}_9$
• Extended geometries
• E${}_9$ exceptional field theory I. The potential
• A master exceptional field theory
• On supersymmetric E11 exceptional field theory
• E${}_9$ exceptional field theory II. The complete dynamics
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• $L_{\infty }$ algebras for extended geometry from Borcherds superalgebras
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• Tensor hierarchy algebras and extended geometry I: Construction of the algebra
• Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras
• A Riemann-Hilbert approach to rotating attractors
• Generators and relations for Lie superalgebras of Cartan type
• Infinity-enhancing of Leibniz algebras
• Exploring the geometry of supersymmetric double field theory
• Generalized Dualities and Supergroups
• Symmetries of M-theory and free Lie superalgebras
• Maximal D=2 supergravities from higher dimensions
• Teleparallelism in the algebraic approach to extended geometry
• Exceptional field theories, superparticles in an enlarged 11D superspace and higher spin theories
• The E10 Wheeler-DeWitt operator at low levels
• SL(5) supersymmetry
• The different faces of branes in Double Field Theory
• Extended geometry of magical supergravities
• Type II Double Field Theory in Superspace
• $L_{\infty }$ algebras for extended geometry
• Unfolding $E_{11}$
• Aspects of electric-magnetic dualities in maximal supergravity
• Exceptional Periodicity and Magic Star Algebras. I : Foundations