Abstract
We show that the dilaton beta-function equation in such asigma-model has the form of a stochastic Langevin equation withnon-Markovian noise. The worldsheet cut-off is identified with stochastictime and the V5-operator plays the role of the noise. We derive theFokker-Planck equation associated with this stochastic process andshow that the Hamiltonian of the AdS5 supergravity defines thedistribution satisfying this Fokker-Planck equation. This means that thedynamical compactification of the spacetime on AdS5×{S5}occurs as a result of the non-Markovian stochastic process, generated bythe V5-operator noise. This provides us with an insight into relationsbetween the holography principle and the concept of stochastic quantizationfrom the point of view of critical string theory.
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