Holographic RG flows for four-dimensional $$ \mathcal{N}=2 $$ SCFTs

Abstract

Abstract We study holographic renormalization group flows from four-dimensional $$ \mathcal{N}=2 $$ N = 2 SCFTs to either $$ \mathcal{N}=2 $$ N = 2 or $$ \mathcal{N}=1 $$ N = 1 SCFTs. Our approach is based on the framework of five-dimensional half-maximal supergravity with general gauging, which we use to study domain wall solutions interpolating between different supersymmetric AdS5 vacua. We show that a holographic RG flow connecting two $$ \mathcal{N}=2 $$ N = 2 SCFTs is only possible if the flavor symmetry of the UV theory admits an SO(3) subgroup. In this case the ratio of the IR and UV central charges satisfies a universal relation which we also establish in field theory. In addition we provide several general examples of holographic flows from $$ \mathcal{N}=2 $$ N = 2 to $$ \mathcal{N}=1 $$ N = 1 SCFTs and relate the ratio of the UV and IR central charges to the conformal dimension of the operator triggering the flow. Instrumental to our analysis is a derivation of the general conditions for AdS vacua preserving eight supercharges as well as for domain wall solutions preserving eight Poincaré supercharges in half-maximal supergravity.