How to go with an RG Flow

TL;DR

The paper develops a consistent holographic renormalization approach to compute one- and two-point functions of the stress-energy tensor and a mixing scalar operator for holographic RG flows in domain-wall backgrounds. By carefully regularizing the on-shell action and adding SUSY-compatible counterterms, the authors extract finite vevs and establish Ward identities with correct conformal anomalies, for both Coulomb-branch and GPPZ flows. The CB flow exhibits a massless dilaton pole in correlators, signaling spontaneous conformal breaking, along with a mass-gap in the spectrum, while the GPPZ flow shows no such pole, reflecting explicit breaking and a discrete spectrum with a mass gap. The work provides a concrete, gauge-invariant framework to obtain physically meaningful correlation functions in holographic RG flows and suggests extensions to other operators and CS equations.

Abstract

We apply the formalism of holographic renormalization to domain wall solutions of 5-dimensional supergravity which are dual to deformed conformal field theories in 4 dimensions. We carefully compute one- and two-point functions of the energy-momentum tensor and the scalar operator mixing with it in two specific holographic flows, resolving previous difficulties with these correlation functions. As expected, two-point functions have a 0-mass dilaton pole for the Coulomb branch flow in which conformal symmetry is broken spontaneously but not for the flow dual to a mass deformation in which it is broken explicitly. A previous puzzle of the energy scale in the Coulomb branch flow is explained.