Null Deformed Domain Wall

TL;DR

This paper classifies null deformations of flat domain wall solutions in N=2, d=5 gauged supergravity, revealing their origins, properties, and potential holographic applications, with explicit solutions and a systematic construction approach.

Contribution

It provides a comprehensive classification of null deformations in gauged supergravity domain walls, distinguishing gauging and non-gauging types, and discusses explicit solution construction methods.

Findings

Deformations originate from hypermultiplet sector or are null.

Deformations organize into v-deformations and u-deformations.

Explicit solutions and holographic implications are discussed.

Abstract

We study null 1/4 BPS deformations of flat domain wall solutions (NDDW) in N=2, d=5 gauged supergravity with hypermultiplets and vector multiplets coupled. These are uncharged time-dependent configurations and contain as special case, 1/2 supersymmetric flat domain walls (DW), as well as 1/2 BPS null solutions of the ungauged supergravity. Combining our analysis with the classification method initiated by Gauntlett et al., we prove that all the possible deformations of the DW have origin in the hypermultiplet sector or/and are null. Here, we classify all the null deformations: we show that they naturally organize themselves into "gauging" (v-deformation) and "non gauging" (u-deformation). They have different properties: only in presence of v-deformation is the solution supported by a time-dependent scalar potential. Furthermore we show that the number of possible deformations equals the number of matter multiplets coupled. We discuss the general procedure for constructing explicit solutions, stressing the crucial role taken by the integrability conditions of the scalars as spacetime functions. Two analytical solutions are presented. Finally, we comment on the holographic applications of the NDDW, in relation to the recently proposed time-dependent AdS/CFT.