Correlation Functions in Holographic Renormalization Group Flows

TL;DR

This paper develops a method to compute all one- and two-point functions in holographic RG flows by analyzing scalar and metric fluctuations around Poincare invariant backgrounds, confirming field theory expectations.

Contribution

It introduces a comprehensive approach to derive correlation functions in holographic RG flows considering independent boundary conditions for scalars and metrics.

Findings

Successfully computes correlation functions for GPPZ and Coulomb branch flows.

Distinguishes operator and vev flows via physical condensates.

Confirms consistency with field theoretical predictions.

Abstract

We consider the holographic duality for a generic bulk theory of scalars coupled to gravity. By studying the fluctuations around Poincare invariant backgrounds with non-vanishing scalars, with the scalar and metric boundary conditions considered as being independent, we obtain all one- and two-point functions in the dual renormalization group flows of the boundary field theory. Operator and vev flows are explicitly distinguished by means of the physical condensates. The method is applied to the GPPZ and Coulomb branch flows, and field theoretical expectations are confirmed.