The maximal D=7 supergravities

Abstract

The general seven-dimensional maximal supergravity is presented. Its universal Lagrangian is described in terms of an embedding tensor which can be characterized group-theoretically. The theory generically combines vector, two-form and three-form tensor fields that transform into each other under an intricate set of nonabelian gauge transformations. The embedding tensor encodes the proper distribution of the degrees of freedom among these fields. In addition to the kinetic terms the vector and tensor fields contribute to the Lagrangian with a unique gauge invariant Chern-Simons term. This new formulation encompasses all possible gaugings. Examples include the sphere reductions of M theory and of the type IIA/IIB theories with gauge groups SO(5), CSO(4,1), and SO(4), respectively.

42 pages

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Cited by in corpus (85)

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• Exceptional field theory: $SL(5)$
• Exceptional field theory: $SO(5,5)$
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• Flux Compactifications of M-Theory on Twisted Tori
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• Gauging Maximal Supergravities
• The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge Theories
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• Supersymmetric Domain Walls
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• The supersymmetric tensor hierarchy of N=1,d=4 supergravity
• Supergravity and M-Theory
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• Introductory Lectures on Extended Supergravities and Gaugings
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• Local E(11) and the gauging of the trombone symmetry
• Maximal D=2 supergravities from higher dimensions
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• Geometric non-geometry
• A geometric formulation of exceptional field theory
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• Exotic potentials and Bianchi identities in SL(5) exceptional field theory
• On gauged maximal d=8 supergravities
• Dualising consistent truncations
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• New methods for old problems: vacua of maximal D = 7 supergravities
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• Supersymmetric quantum mechanics from wrapped D4-branes
• Holographic RG flows in N=4 SCFTs from half-maximal gauged supergravity
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• $E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies