Domain-wall supergravities from sphere reduction

Kaluza-Klein sphere reductions of supergravities that admit AdS x Sphere vacuum solutions are believed to be consistent. The examples include the S-4 and S-7 reductions of eleven-dimensional supergravity, and the S-5 reduction of ten-dimensional type IIB supergravity. In this paper we provide evidence that sphere reductions of supergravities that admit instead Domain-wallxSphere vacuum solutions are also consistent, where the background can be viewed as the near-horizon structure of a dilatonic p-brane of the theory. The resulting lower-dimensional theory is a gauged supergravity that admits a domain wall, rather than AdS, as a vacuum solution. We illustrate this consistency by taking the singular limits of certain modulus parameters, for which the original S-n compactifying spheres (n = 4, 5 or 7) become S-P x R-q, With p = n - q < n. The consistency of the S-4, S-7 and S-5 reductions then implies the consistency of the SP reductions of the lower-dimensional supergravities. In particular, we obtain explicit non-linear ansatze for the S-3 reduction of type IIA and heterotic supergravities, restricting to the U(1)(2) subgroup of the SO(4) gauge group of S3. We also study the black-hole solutions in the lower-dimensional gauged supergravities with domain-wall backgrounds. We find new domain-wall black holes which are not the singular-modulus limits of the AdS black holes of the original theories, and we obtain their Killing spinors, (C) 1999 Elsevier Science B,V, All rights reserved.