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On Lagrangians and Gaugings of Maximal Supergravities
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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) 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.
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How to uplift non-maximal gauged supergravities
An ExFT-based algorithm reduces the uplift problem to a PDE on the base of the internal manifold and classifies the type IIB uplifts of pure SO(4)-gauged N=4 supergravity by two harmonic functions on a Riemann surface.
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