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.
In this note we discuss the classification of duality orbits of N=8 gauged supergravity models. Using tensor classifiers, we show that there is a one-parameter family of inequivalent SO(8) gauged supergravity theories. We briefly discuss the couplings of such models and show that, although the maximally symmetric vacuum has the same quadratic spectrum, the supersymmetry transformations, the couplings, and the scalar potential are parameter dependent. We also comment on the possible M theory uplift and on the meaning of the parameter for the dual gauge theories.
We present the main features of the physics of extremal black holes embedded in supersymmetric theories of gravitation, with a detailed analysis of the attractor mechanism for BPS and non-BPS black-hole solutions in four dimensions.
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