How to go with an RG Flow

TL;DR

This paper uses holographic renormalization to analyze domain wall solutions in 5D supergravity, computing correlation functions in dual 4D theories and clarifying the nature of conformal symmetry breaking.

Contribution

It provides detailed calculations of correlation functions in specific holographic flows, resolving previous issues and clarifying the role of the dilaton pole in symmetry breaking.

Findings

Two-point functions exhibit a dilaton pole in spontaneous symmetry breaking.

Explicit symmetry breaking flows lack the dilaton pole.

The energy scale puzzle in Coulomb branch flow is resolved.

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.