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

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.