M‐theory and gauged supergravities

We present a pedagogical discussion of the emergence of gauged supergravities from M‐theory. First, a review of maximal supergravity and its global symmetries and supersymmetric solutions is given. Next, different procedures of dimensional reduction are explained: reductions over a torus, a group manifold and a coset manifold and reductions with a twist. Emphasis is placed on the consistency of the truncations, the resulting gaugings and the possibility to generate field equations without an action. Using these techniques, we construct a number of gauged maximal supergravities in diverse dimensions with a string or M‐theory origin. One class consists of the CSO gaugings, which comprise the analytic continuations and group contractions of SO ( n ) gaugings. We construct the corresponding half‐supersymmetric domain walls and discuss their uplift to D‐ and M‐brane distributions. Furthermore, a number of gauged maximal supergravities are constructed that do not have an action.