On Lagrangians and gaugings of maximal supergravities

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. (C) 2003 Elsevier Science B.V. All rights reserved.