On Lagrangians and gaugings of maximal supergravities

By B. Wit, H. Samtleben, Mario Trigiante. 2002

340 citations recorded by the source corpus.

A consistent gauging of maximal supergravity requires that the T-tensor transforms according to a specific representation of the duality group. The analysis of viable gaugings is thus amenable to group-theoretical analysis, which we explain and exploit for a large variety of gaugings. We discuss the subtleties in four spacetime dimensions, where the ungauged Lagrangians are not unique and encoded in an matrix. Here we define the T-tensor and derive all relevant identities in full generality. We present a large number of examples in d=4,5 spacetime dimensions which include non-semisimple gaugings of the type arising in (multiple) Scherk–Schwarz reductions. We also present some general background material on the latter as well as some group-theoretical results which are necessary for using computer algebra.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1c27cb05aaf56cd2cb2e511142cfd780f6f95157

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Citations in the corpus

Anomalies, anomalous U(1)'s and generalized Chern-Simons terms (2006, neutral): “Contents”
Gauged locally supersymmetric D=3 nonlinear sigma models (2003, background): “es the so-called T-tensors. The viability of the gauging depends in a subtle manner on the properties of these T-tensors and the gauged supergravity models have an elegant mathematical structure (see [7] for the corresponding analysis of the maximal supergravities in higher dimensions). In this pape”
Lectures on gauged supergravity and flux compactifications (2008, methodology): “struction that is based on the underlying global symmetry group G of the ungauged theory. This framework, rst developed in the context of three-dimensional supergravity [11, 12] and further shaped in [13, 14, 15], encodes the possible gaugings in an embedding tensor that describes the embedding of t”
Spheres, Generalised Parallelisability and Consistent Truncations (2014, methodology): “δ αδβǫ ¯ˆ Eγǫ+δδ βδαǫ ¯ˆ Eγǫ . (3.63) Let us now connect to the consistent truncation. The embedding tensor TABC of four-dimensional N = 8 supergravity transforms in the 912 representation of E7(7) [57]. Decomposing under SL(8,R) this splits as 912= 36+36′ +420+420′. (3.64) For the SO(8) gauging, o”
Extended geometry and gauged maximal supergravity (2013, methodology): “are contractions of the embedding tensor (which dictates how the gauge group is embedded in the global symmetry group) with the generators of the global symmetry group [23].”
On the vacua of N=8 gauged supergravity in 4 dimensions (2011, methodology): “In this paper we will show how, by combining the embedding tensor formalism, applied to N = 8 supergravity in [2, 3], and the fact that the scalar manifold is a coset space, the conditions to produce vacua of gauged N = 8 supergravity can be reduced to a combination of linear and quadratic constrain”
Gauged maximal supergravities and hierarchies of nonabelian vector‐tensor systems (2005, neutral): “ar X iv :h ep -t h/ 05 01 24 3v 2”
Gauged Supergravities. (2016, methodology): “In this appendix, taken form [152], we explicitly construct the projectors onto the irreducible representations in the tensor product of the fundamental with the adjoint representation of an arbitrary simple group G.”
Magnetic charges in local field theory (2005, methodology): “Of course, this invariance is only realized provided that also the field equations associated with fields other than the gauge fields, will respect the invariance.”
The E-11 origin of all maximal supergravities (2007, background): “The fact that the most general gauged maximal six-dimensional supergravity arises from a mass deformation belonging to the 144 of SO(5, 5) has been shown in [19].”
The maximal D = 4 supergravities (2007, methodology): “Z(x), or by absorbing an GL(28) transformation emerging on the left into the deﬁnition of the gauge ﬁelds. The ambiguity thus takes the form of an E7(7)\Sp(56;R)/GL(28) matrix (or rather its inverse) [23, 7]. The Lagrangian will implicitly depend on this matrix, as it will be written in terms of VΛi”
Double field theory: a pedagogical review (2013, positive): “The projectors onto the first two representations in this product are given by [93] P(56)M , β = 56 133 (ttβ )M, P(912)M , β = (1)7δα βδ M − 12 7 (tβt )M + (4)7 (ttβ )M .”
Consistent Kaluza-Klein truncations via exceptional field theory (2014, neutral): “[50].”