Stochastic quantization of conformally coupled scalar in AdS

TL;DR

This paper investigates the connection between stochastic quantization and holographic RG flow by analyzing a conformally coupled scalar in AdS, establishing a precise mapping between radial flow and stochastic correlation functions.

Contribution

It demonstrates a one-to-one correspondence between the radial flow of double trace deformations and stochastic 2-point functions for a conformally coupled scalar in AdS, confirming previous proposals.

Findings

Established a direct mapping between holographic RG flow and stochastic quantization.

Confirmed the equivalence up to a field redefinition of the bulk scalar.

Extended the understanding of stochastic holography in AdS/CFT contexts.

Abstract

We explore the relation between stochastic quantization and holographic Wilsonian renormalization group flow further by studying conformally coupled scalar in $AdS_{d+1}$. We establish one to one mapping between the radial flow of its double trace deformation and stochastic 2-point correlation function. This map is shown to be identical, up to a suitable field re-definition of the bulk scalar, to the original proposal in arXiv:1209.2242.