On Lagrangians and gaugings of maximal supergravities

Abstract

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 E 7(7) \Sp(56; R)/GL(28) 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) ScherkSchwarz 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.

Supersymmetric completion of M-theory 4D-gauge algebra from twisted tori and fluxes

“…Supersymmetry and closure of the gauge algebra inside E 7(7) require a linear and a quadratic condition in θ respectively [35,36]:…”

“…The resulting gauged supergravity [21] is defined by an embedding tensor transforming in the 78 +3 [35] with respect to the E 6(6) × O(1, 1) subgroup of E 7 (7) . In the basis of the 56 in which the 28 electric vector fields are A Λ µ = {A u µ , A 0 µ }, where A u µ , u = 1, .…”

The maximal supergravities

“…Over recent years it has emerged that the structures of supergravity theories with a maximal number of supercharges are far richer than originally anticipated [1,2,3,4]. Maximal supergravities are obtained as deformations (gaugings) of toroidally compactified eleven-dimensional supergravity by coupling the initially abelian vector fields to charges assigned to the elementary fields.…”

“…The specific form of the embedding tensor in a particular gauging encodes the proper distribution of the degrees of freedom among these fields. Together, this gave rise to a universal formulation of the maximal supergravities in various space-time dimensions [1,2,3,4], capturing all possible supersymmetric deformations in a manifestly G-covariant way. Although most of this formalism has been established for the global symmetry groups G = E d(d) of the maximal supergravities the structures are not restricted to maximal supersymmetry and similarly underlay the theories with lower number of supercharges.…”

“…This theory is formulated entirely in terms of vector and two-form tensor fields, transforming in the 10 and the 5 representation of SL(5), respectively. The first gaugings in D = 7 were constructed in [6,7] with semisimple gauge groups SO(5), SO (4,1), and SO (3,2). Notably, the SO(5) theory corresponds to compactification of D = 11 supergravity on the sphere S 4 .…”