Kac-Moody Spectrum of (Half-)Maximal Supergravities

Abstract

We establish the correspondence between, on one side, the possible gaugings and massive deformations of half-maximal supergravity coupled to vector multiplets and, on the other side, certain generators of the associated very extended Kac-Moody algebras. The difference between generators associated to gaugings and to massive deformations is pointed out. Furthermore, we argue that another set of generators are related to the so-called quadratic constraints of the embedding tensor. Special emphasis is placed on a truncation of the Kac-Moody algebra that is related to the bosonic gauge transformations of supergravity. We give a separate discussion of this truncation when non-zero deformations are present. The new insights are also illustrated in the context of maximal supergravity.

Added references, published version

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• E(11) and the Embedding Tensor
• IIA Ten-forms and the Gauge Algebras of Maximal Supergravity Theories
• Dual fields and E_{11}
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Cited by in corpus (16)

• Lectures on Gauged Supergravity and Flux Compactifications
• Duality orbits of non-geometric fluxes
• Half-maximal supersymmetry from exceptional field theory
• Gauge Theories, Duality Relations and the Tensor Hierarchy
• Multiple M2-branes and the Embedding Tensor
• Twin Supergravities
• Local E(11)
• The supersymmetric tensor hierarchy of N=1,d=4 supergravity
• Forms and algebras in (half-)maximal supergravity theories
• Supersymmetric $Ad{S}_6$ vacua in six-dimensional $N=(1,1)$ gauged supergravity
• A Note on E11 and Three-dimensional Gauged Supergravity
• Gaugings at angles from orientifold reductions
• E10 and Gauged Maximal Supergravity
• Maximal Nine Dimensional Supergravity, General gaugings and the Embedding Tensor
• Gauged Supergravities and the Physics of Extra Dimensions
• Borcherds and Kac-Moody extensions of simple finite-dimensional Lie algebras