AdS/CFT Correspondence, Critical Strings and Stochastic Quantization

TL;DR

This paper demonstrates that the dilaton beta-function in a brane-like sigma-model can be interpreted as a non-Markovian stochastic process, linking holography and stochastic quantization in the context of AdS/CFT correspondence.

Contribution

It introduces a novel stochastic interpretation of the dilaton beta-function as a Langevin equation with non-Markovian noise, connecting string theory, holography, and stochastic quantization.

Findings

The beta-function equation takes the form of a stochastic Langevin equation.

The Fokker-Planck equation's solution is related to AdS_5 supergravity Hamiltonian.

Dynamical compactification occurs via a non-Markovian stochastic process.

Abstract

We show that dilaton beta-function equation in the brane-like sigma-model (regarded as NSR analogue of string theory on $AdS_5\times{S^5}$) has the form of stochastic Langevin equation with non-Markovian noise. The worldsheet cutoff is identified with stochastic time and the $V_5$-operator plays the role of the noise. We derive the Fokker-Planck equation associated with this stochastic process and show that the Hamiltonian of the $AdS_5$ supergravity defines the distribution satisfying this Fokker-Planck equation. This means that the dynamical compactification of flat ten-dimensional space-time on $AdS_5\times{S^5}$ occurs as a result of the non-Markovian stochastic process, generated by the $V_5$-operator noise. This provides us with an insight into relation between holography principle and the concept of stochastic quantization from the point of view of critical string theory.