Holographic RG Flows for Four-dimensional $\mathcal{N}=2$ SCFTs

TL;DR

This paper explores holographic renormalization group flows between four-dimensional $ abla=2$ SCFTs using five-dimensional supergravity, revealing conditions for flows and relations between central charges and operator dimensions.

Contribution

It introduces a framework for analyzing supersymmetric RG flows in holography, establishing universal relations and conditions for flows between $ abla=2$ SCFTs.

Findings

Flow between two $ abla=2$ SCFTs requires an ${ m SO}(3)$ flavor subgroup.

Universal relation between IR and UV central charges for $ abla=2$ to $ abla=2$ flows.

Relation between central charge ratios and operator conformal dimensions.

Abstract

We study holographic renormalization group flows from four-dimensional $\mathcal{N}=2$ SCFTs to either $\mathcal{N}=2$ or $\mathcal{N}=1$ 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 AdS$_5$ vacua. We show that a holographic RG flow connecting two $\mathcal{N}=2$ SCFTs is only possible if the flavor symmetry of the UV theory admits an ${\rm SO}(3)$ 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 $\mathcal{N}=2$ to $\mathcal{N}=1$ 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 Poincare supercharges in half-maximal supergravity.