Stochastic Quantization and AdS/CFT

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.