The Domain Walls of Gauged Maximal Supergravities and their M-theory Origin

We consider gauged maximal supergravities with CSO(p,q,r) gauge groups and their relation to the branes of string and M-theory. The gauge groups are characterised by n mass parameters, where n is the transverse dimension of the brane. We give the scalar potentials and construct the corresponding domain wall solutions. In addition, we show the higher-dimensional origin of the domain walls in terms of (distributions of) branes. We put particular emphasis on the CSO(p,q,r) gauged supergravities in D=9 and D=8, which are related to the D7-brane and D6-brane, respectively. In these cases, twisted and group manifold reductions are shown to play a crucial role. We also discuss salient features of the corresponding brane distributions.