Domain Walls from Anti-de Sitter Spacetime

We examine $(D-2)$-brane solutions in supergravities, showing that they fall into three categories depending on the details of the dilaton coupling. In general they describe domain walls, although in one of the three categories the metric describes anti-de Sitter spacetime. We study this case, and its $S^1$ dimensional reduction to a more conventional domain wall in detail, focussing in particular on the manner in which the unbroken supersymmetry of the anti-de Sitter solution is partially broken by the dimensional reduction to the domain wall.