Stochastic Quantization and AdS/CFT

TL;DR

This paper explores a proposed connection between stochastic quantization and AdS/CFT correspondence, demonstrating a specific scalar field relationship in AdS4 and 3d, supported by explicit calculations and geometric insights.

Contribution

It provides the first explicit calculation linking stochastic quantization with AdS/CFT, revealing a geometric origin for their relationship.

Findings

A conformally coupled scalar in AdS4 with phi4 interaction relates to a massless scalar with phi6 interaction in 3d.

The relationship between stochastic quantization and AdS/CFT is supported by explicit calculations.

Results suggest an underlying geometric origin for the stochastic quantization and holography connection.

Abstract

We argue that there is a relationship between stochastic quantization and AdS/CFT, and we present an explicit calculation to support our claim. In particular, we show that a conformally coupled scalar with phi4 interaction on AdS4 is related, via stochastic quantization as well as via AdS/CFT, to a massless scalar with phi6 interaction in 3d. We show that our results have an underlying geometric origin, which might help to elucidate further the proposed relationship between stochastic quantization and holography.