Domain-wall Supergravities from Sphere Reduction

TL;DR

This work demonstrates that sphere reductions of supergravities with domain-wall$\times$Sphere vacua are conceptually and technically consistent, extending the well-known AdS$\times$Sphere reductions. By taking singular modulus limits of $S^n$ to $S^p\times \mathbb{R}^q$, the authors derive domain-wall gauged supergravities in $D=7,4,5$ and construct explicit non-linear reduction Ansätze (notably for $S^3$ reductions in IIA and heterotic theories). They uncover new domain-wall black-hole solutions and analyze their Killing spinors, showing how AdS black-hole physics generalizes to domain-wall spacetimes in these lower-dimensional theories. The results illuminate a geometric and holographic link between higher-dimensional brane near-horizon structures and lower-dimensional domain-wall dynamics, with potential implications for domain-wall/QFT dualities.

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.