How to go with an RG Flow

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.