Curved Domain Walls of Five Dimensional Gauged Supergravity

TL;DR

This paper investigates curved domain wall solutions in five-dimensional gauged supergravity, revealing conditions under which supersymmetry permits curved worldvolumes and the constraints imposed by equations of motion.

Contribution

It provides a comprehensive analysis of curved domain walls in gauged supergravity, including flux effects and generalizations beyond specific compactifications.

Findings

Supersymmetry allows curved domain walls with a cosmological constant.

Equations of motion restrict solutions to Ricci-flat worldvolumes under certain conditions.

Non-supersymmetric solutions exist with Einstein manifold worldvolumes in flux-free cases.

Abstract

We study curved domain wall solutions for gauged supergravity theories obtained by gauging some of the isometries of the manifold spanned by the scalars of vector and hypermultiplets. We first consider the case obtained by compactifying M-theory on a Calabi-Yau threefold in the presence of G-fluxes. It is found that supersymmetry allows for the construction of domain wall configurations with curved worldvolume and a cosmological constant. However it turns out that the equations of motion, if one insists on the supersymmetric ansatz for the scalars and warp factor, rule out solutions with a cosmological constant and allows only for Ricci-flat worldvolumes. Moreover, in the absence of flux, there are non-supersymmetric solutions with worldvolumes given by Einstein manifolds. We also generalize our results to all five dimensional gauged supergravity.