Domain - wall Supergravities from Sphere Reduction

Kaluza-Klein sphere reductions of supergravities that admit AdS×Sphere vacuum solutions are believed to be consistent. The examples include the S4 and S7 reductions of eleven-dimensional supergravity, and the S5 reduction of ten-dimensional type IIB supergravity. In this paper we provide evidence that sphere reductions of supergravities that admit instead Domain-wall×Sphere 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 Sn compactifying spheres (n = 4, 5 or 7) become Sp × Rq, with p = n − q < n. The consistency of the S4, S7 and S5 reductions then implies the consistency of the Sp reductions of the lower-dimensional supergravities. In particular, we obtain explicit non-linear ansätze for the S3 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. 1 Research supported in part by DOE grant DOE-FG02-95ER40893 2 Research supported in part by DOE grant DOE-91ER40651-TASKB 3 Research supported in part by DOE grant DOE-FG03-95ER40917