A note on gravity-scalar fluctuations in holographic RG flow geometries

TL;DR

The paper addresses calculating correlation functions in five-dimensional gravity models dual to RG-flow boundary theories with active scalars. It introduces an almost radial gauge that decouples the graviton trace from scalar fluctuations and derives a simple quadratic action for the trace, related to a scalar via $h \sim \beta^{-1}s$, with the action scaled by $\beta^2$. This framework is applied to two explicit kink backgrounds (GPPZ-type flow and a Coulomb-branch flow), yielding a discrete spectrum in the first case and a continuous spectrum with a mass gap in the second, aligning with expectations for inert scalars and UV AdS behavior with $\Delta=2$. The work clarifies the operator duals, showing $T_i^i=\beta\mathcal{O}$, and demonstrates the method’s resilience even in the presence of interior singularities, by leveraging the Hamiltonian AdS/CFT prescription.

Abstract

We study five-dimensional gravity models with non-vanishing background scalar fields which are dual to non-conformal boundary field theories. We develop a procedure to decouple the graviton fluctuations from the scalar ones and apply it to the simplest case of one scalar field. The quadratic action for the decoupled scalar fluctuations has a very simple form and can be used to compute two-point functions. We perform this computation for the two examples of background RG flow recently considered by DeWolfe and Freedman and find physically reasonable results.