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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have