Domain-wall Supergravities from Sphere Reduction

TL;DR

This paper demonstrates the consistency of sphere reductions in supergravity theories that admit domain-wall solutions, extending known results from AdS vacua to domain-wall backgrounds, and constructs explicit reduction ansatze and black hole solutions.

Contribution

It provides evidence that sphere reductions leading to domain-wall vacua are consistent, including explicit non-linear ansatze and new black hole solutions in lower-dimensional supergravities.

Findings

Sphere reductions to domain-wall vacua are consistent.

Explicit S^3 reduction ansatz for type IIA and heterotic supergravities.

New domain-wall black hole solutions with Killing spinors.

Abstract

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-wall x 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 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 S^p 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 S^3. 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.