Einstein Brane-Worlds In 5D Gauged Supergravity

TL;DR

This work addresses whether Einstein domain walls with four-dimensional negative-curvature worldvolumes can be embedded in five-dimensional $N=2$ gauged supergravity with vector and hypermultiplets. The authors derive first-order flow equations for scalar fields from a generalized Killing-spinor projection and test their compatibility with the full equations of motion, identifying the conditions under which curved domain walls can exist. They show that, to satisfy both supersymmetry and dynamics, stringent restrictions such as $ abla_X W = 0$ and $ abla_X oldsymbol{A} = 0$ are required, and they relate the warp factor $U(z)$ and the superpotential $W$ through a function $G(W)$ and a function $f(W) = g^{xy} abla_x W abla_y W$. The results extend previous flat/ricci-flat domain wall constructions to Einstein walls in $N=2$ gauged supergravity and provide a framework for explicit model-building and future extensions to four dimensions and worldvolume gauge dynamics.

Abstract

We study, in the context of five dimensional N=2 gauged supergravity with vector and hypermultiplets, curved domain wall solutions with worldvolumes given by four dimensional Einstein manifolds. For a choice of the projection condition on the Killing spinors of the BPS solutions, first order differential equations governing the flow of the scalars are derived. With these equations, we analyze the equations of motion and determine conditions under which gauged supergravity theories may admit Einstein domain wall solutions.