AdS/CFT correspondence, critical strings and stochastic quantization

We show that the dilaton beta-function equation in such a sigma-model has t he form of a stochastic Langevin equation with non-Markovian noise. The wor ldsheet cut-off is identified with stochastic time and the V-5-operator pla ys the role of the noise. We derive the Fokker-Planck equation associated w ith this stochastic process and show that the Hamiltonian of the AdS(5) sup ergravity defines the distribution satisfying this Fokker-Planck equation. This means that the dynamical compactification of the spacetime on AdS(5) x S-5 occurs as a result of the non-Markovian stochastic process, generated by the Vs-operator noise. This provides us with an insight into relations b etween the holography principle and the concept of stochastic quantization from the point of view of critical string theory.