The holographic RG flow in a field theory on a curved background

TL;DR

This paper extends the holographic RG flow framework to supersymmetric field theories on curved $AdS_4$ backgrounds, constructing a curved domain wall solution that models the RG flow in this setting.

Contribution

It introduces a curved supersymmetric domain wall solution describing RG flows in supersymmetric field theories on curved backgrounds, generalizing previous flat background models.

Findings

Constructed a curved supersymmetric domain wall solution.

Demonstrated holographic RG flows on curved $AdS_4$ backgrounds.

Showed that curved domain walls can describe RG flows in curved spacetime.

Abstract

As shown by Freedman, Gubser, Pilch and Warner, the RG flow in ${\cal N}=4$ super-Yang-Mills theory broken to an ${\cal N}=1$ theory by the addition of a mass term can be described in terms of a supersymmetric domain wall solution in five-dimensional ${\cal N}=8$ gauged supergravity. The FGPW flow is an example of a holographic RG flow in a field theory on a flat background. Here we put the field theory studied by Freedman, Gubser, Pilch and Warner on a curved $AdS_4$ background, and we construct the supersymmetric domain wall solution which describes the RG flow in this field theory. This solution is a curved (non Ricci flat) domain wall solution. This example demonstrates that holographic RG flows in supersymmetric field theories on a curved $AdS_4$ background can be described in terms of curved supersymmetric domain wall solutions.