Domain walls in five dimensional supergravity with non-trivial hypermultiplets

TL;DR

The paper investigates BPS domain walls in five-dimensional $N=2$ gauged supergravity with non-trivial hypermultiplets, formulating supersymmetric flow equations and a monotonic c-function to describe holographic RG-flows between $AdS_5$ vacua. A generalized $SU(2)_R$ gauging with a $q$-dependent prepotential $\widehat{P}_I^A(q)$ is introduced, yielding a gradient-flow structure for scalar fields with a superpotential $W$ controlling the flows: $\beta^M = -3\,g^{MN}\partial_N\log W$ and $C(\mu) = C_0/|W|^3$ with $\frac{dC}{d\mu} > 0$. An explicit example demonstrates the recovery of the Freedman–Gubser–Pilch–Warner RG-flow by suitable Abelian gaugings and $q$-dependent gauging, highlighting the necessity of hypermultiplet effects for IR fixed points and, potentially, supersymmetric Randall–Sundrum walls. The results illuminate how IR fixed points arise in holographic RG-flows with hypermultiplets and point toward broader implications for RS-type constructions and M-theory embeddings.

Abstract

We study BPS domain wall solutions of 5-dimensional N=2 supergravity where isometries of the hypermultiplet geometry have been gauged. We derive the corresponding supersymmetric flow equations and define an appropriate c-function. As an example we discuss a domain wall solution of Freedman, Gubser, Pilch and Warner which is related to a RG-flow in a dual superconformal field theory.