The gauge structure of Exceptional Field Theories and the tensor hierarchy

Abstract

We address the construction of manifest U-duality invariant generalized diffeomorphisms. The closure of the algebra requires an extension of the tangent space to include a tensor hierarchy indicating the existence of an underlying unifying structure, compatible with E_{11} and Borcherds algebras constructions. We begin with four-dimensional gauged maximal supergravity, and build a generalized Lie derivative that encodes all the gauge transformations of the theory. A generalized frame is introduced, which accommodates for all the degrees of freedom, including the tensor hierarchy. The generalized Lie derivative defines generalized field-dependent fluxes containing all the covariant quantities in the theory, and the closure conditions give rise to their corresponding Bianchi Identities. We then move towards the construction of a full generalized Lie derivative defined on an extended space, analyze the closure conditions, and explore the connection with that of maximal gauged supergravity via a generalized Scherk-Schwarz reduction, and with 11-dimensional supergravity.

53 pages

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• Gauge Theories, Duality Relations and the Tensor Hierarchy
• U-dual fluxes and Generalized Geometry
• The E(11) origin of all maximal supergravities - the hierarchy of field-strengths
• Gauging hidden symmetries in two dimensions
• Gauged Supergravities in Various Spacetime Dimensions
• Exceptional geometry and tensor fields
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• Strings and Branes are Waves
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• The Geometry, Branes and Applications of Exceptional Field Theory
• U-duality extension of Drinfel'd double
• The geometry behind double geometry
• Loops in exceptional field theory
• Supersymmetric Backgrounds and Generalised Special Holonomy
• A master exceptional field theory
• Double Field Theory at SL(2) angles
• Seeking the balance: Patching double and exceptional field theories
• The Exceptional Sigma Model
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Generalised Space-time and Gauge Transformations
• Uplifting non-compact gauged supergravities
• Exceptional geometry and Borcherds superalgebras
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• On the exceptional generalised Lie derivative for $d\ge 7$
• Einstein-Cartan Calculus for Exceptional Geometry
• Cosmological Implications from O(D,D)
• Cancellation of divergences up to three loops in exceptional field theory
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Lobotomy of Flux Compactifications
• Gaugings from E7 Extended Geometries
• Locally non-geometric fluxes and missing momenta in M-theory
• U-gravity : $\mathbf{SL}(N)$
• E11 and exceptional field theory
• Connecting M-theory and type IIB parameterizations in Exceptional Field Theory
• Maximal D=2 supergravities from higher dimensions
• New N=1 AdS${}_4$ solutions of type IIB supergravity
• Finite Transformations in Doubled and Exceptional Space
• Gauge Transformation of Double Field Theory for Open String
• Gauge symmetry enhancing-breaking from a Double Field Theory perspective
• Dimensional Reduction of the Generalized DBI
• Twistors and supertwistors for exceptional field theory
• Generalized Cartan Calculus in general dimension
• Reductions of Exceptional Field Theories
• C-spaces, generalized geometry and double field theory
• Duality Covariant Solutions in Extended Field Theories
• $E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies
• Exotic Aspects of Extended Field Theories