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arXiv · 1312.4549

The gauge structure of Exceptional Field Theories and the tensor hierarchy

Gerardo Aldazabal·Mariana Graña·Diego Marqués·José A. Rosabal
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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. 2014-03-10. The gauge structure of Exceptional Field Theories and the tensor hierarchy. https://doi.org/10.1007/jhep04(2014)049

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