Notes on Fluctuations and Correlation Functions in Holographic Renormalization Group Flows

TL;DR

This paper investigates scalar and metric fluctuations in holographic RG flows within N=8 supergravity, developing methods to decouple equations and compute correlation functions, with implications for stability and holographic dualities.

Contribution

It introduces a procedure to decouple coupled scalar-gravity fluctuation equations and provides new examples of correlators in holographic RG flows.

Findings

Successfully decoupled fluctuation equations for single scalar variations.

Provided new correlator examples for simpler bulk scalars.

Discussed stability and Hamilton-Jacobi aspects of holographic RG flows.

Abstract

We study the coupled equations describing fluctuations of scalars and the metric about background solutions of N=8 gauged supergravity which are dual to boundary field theories with renormalization group flow. For the case of a kink solution with a single varying scalar, we develop a procedure to decouple the equations, and we solve them in particular examples. However, difficulties occur in the calculation of correlation functions from the fluctuations, presumably because the AdS/CFT correspondence has not yet been properly implemented in the coupled scalar-gravity sector. Some new examples of correlators of operators dual to simpler uncoupled bulk scalars are given and are satisfactory. As byproducts of our study we make some observations relevant to the stability of domain walls in the brane-world scenario and to the Hamilton-Jacobi formulation of holographic RG flows.