Correlation Functions in Holographic RG Flows

TL;DR

This paper introduces an efficient Hamiltonian-based method for computing correlation functions in holographic RG flows, simplifying the treatment of infinities and applicable to complex domain wall solutions like Janus.

Contribution

It develops a streamlined holographic renormalization technique focusing on counterterm contributions, improving computational efficiency for correlation functions in RG flows.

Findings

Method simplifies the calculation of 2-point functions.

Applicable to flat and AdS-sliced domain walls.

Successfully analyzed Janus solution correlation functions.

Abstract

We discuss the computation of correlation functions in holographic RG flows. The method utilizes a recently developed Hamiltonian version of holographic renormalization and it is more efficient than previous methods. A significant simplification concerns the treatment of infinities: instead of performing a general analysis of counterterms, we develop a method where only the contribution of counterterms to any given correlator needs to be computed. For instance, the computation of renormalized 2-point functions requires only an analysis at the linearized level. We illustrate the method by discussing flat and AdS-sliced domain walls. In particular, we discuss correlation functions of the Janus solution, a recently discovered non-supersymmetric but stable AdS-sliced domain wall.