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.
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Gerardo Aldazabal, Mariana Graña, Diego Marqués, José A. Rosabal. The gauge structure of Exceptional Field Theories and the tensor hierarchy. Journal of High Energy Physics, Springer Verlag (Germany), 2014, 2014, pp.049. ⟨10.1007/JHEP04(2014)049⟩. ⟨cea-01295486⟩

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