Curved BPS domain wall solutions in five-dimensional gauged supergravity

TL;DR

The paper investigates curved BPS domain wall solutions in five-dimensional ${\cal N}=2$ gauged supergravity, showing that non-constant vector (or vector plus hyper) scalars can support curved walls with an anti-de Sitter-like four-dimensional cosmological constant. The authors derive modified first-order BPS equations for the warp factor and vector scalars that include a gamma factor dependent on the wall curvature scale $l$, and they establish that curved solutions require nontrivial SU(2) phases $Q^s$ so that $\partial_{\tilde{x}} Q^s \neq 0$. They demonstrate that non-constant scalar profiles lead to an AdS-type wall with an independent cosmological constant, and they provide the corresponding flow equations and potential, while leaving a complete hypermultiplet analysis for future work. The work generalizes known flat-domain-wall results, connects with DeWolfe–Freedman–Gubser–Karch findings in 5D gravity, and has potential implications for holographic RG flows across AdS vacua.

Abstract

We analyze the possibility of constructing supersymmetric curved domain wall solutions in five-dimensional ${\cal N}=2$ gauged supergravity, which are supported by non-constant scalar fields belonging either to vector multiplets only or to vector and hypermultiplets. We show that the BPS equations for the warp factor and for the vector scalars are modified by the presence of a four-dimensional cosmological constant on the domain wall, in agreement with earlier results by DeWolfe, Freedman, Gubser and Karch. We also show that the cosmological constant on the domain wall is anti-de Sitter like and that it constitutes an independent quantity, not related to any of the objects appearing in the context of very special geometry.