AdS/CFT Correspondence, Critical Strings and Stochastic Quantization

Abstract

We show that dilaton beta-function equation in the brane-like sigma-model (regarded as NSR analogue of string theory on $Ad{S}_5\times S^5$) 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 $Ad{S}_5$ supergravity defines the distribution satisfying this Fokker-Planck equation. This means that the dynamical compactification of flat ten-dimensional space-time on $Ad{S}_5\times S^5$ 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.

23 pages, TeX. Misprints and typos corrected, references added

References in corpus (4)

• RG-Flow, Gravity and the Cosmological Constant
• Gauge fields - strings duality and the loop equation
• Schwinger-Dyson = Wheeler-DeWitt: gauge theory observables as bulk operators
• Exact Renormalization Group and Loop Equation

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• Hamiltonian of Tensionless Strings with Tensor Central Charge Coordinates
• Stochastic Quantization and AdS/CFT
• BRST Properties of New Superstring States
• Stochastic quantization of conformally coupled scalar in AdS
• Stochastic quantization and holographic Wilsonian renormalization group of scalar theories with arbitrary mass
• DBI Action from Closed Strings and D-brane second Quantization
• Stochastic quantization of a self-interacting nonminimal scalar field in semiclassical gravity
• Ghost-Matter Mixing and Feigenbaum Universality in String Theory
• Stochastic quantization and holographic Wilsonian renormalization group of conformally coupled scalar in AdS${}_4$