Curved BPS domain wall solutions in five-dimensional gauged supergravity

TL;DR

This paper investigates supersymmetric curved domain wall solutions in five-dimensional gauged supergravity, revealing how a four-dimensional cosmological constant influences BPS equations and showing it is an independent anti-de Sitter-like parameter.

Contribution

It demonstrates the modification of BPS equations by the cosmological constant and clarifies its independence from very special geometry in five-dimensional supergravity.

Findings

BPS equations are modified by the four-dimensional cosmological constant.

The cosmological constant on the domain wall is anti-de Sitter like.

The cosmological constant is an independent quantity, not tied to very special geometry.

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.