Domain Walls from Anti-de Sitter Spacetime

TL;DR

The paper analyzes $(D-2)$-brane solutions in $D$-dimensional supergravity, showing they fall into four categories determined by the dilaton coupling through $a^2=\Delta + \frac{2(D-1)}{D-2}$, with a special AdS case at $\Delta=\Delta_{\rm AdS}$. It demonstrates that AdS space in $(D+1)$ dimensions can be dimensionally reduced on $S^1$ to a domain-wall in $D$ dimensions, preserving the bosonic symmetries but breaking half the supersymmetry because only Killing spinors independent of the compact coordinate survive. A consistent Kaluza-Klein reduction is shown to exist even without an $S^1\times M_{D-1}$ vacuum, yielding a domain-wall solution with the same $\Delta$ and a shifted dilaton coupling $a\to -2\alpha$. The paper also develops an elementary dualised formulation with a $D$-form field strength, enabling Minkowski solutions and multi-wall configurations that join different AdS regions and clarifying the relation between domain walls and AdS spacetime.

Abstract

We examine $(D-2)$-brane solutions in supergravities, showing that they fall into four categories depending on the details of the dilaton coupling. In general they describe domain walls, although in one of the four 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.