Stochastic quantization and holographic Wilsonian renormalization group

Abstract

We study relation between stochastic quantization and holographic Wilsonian renormalization group flow. Considering stochastic quantization of the boundary on-shell actions with the Dirichlet boundary condition for certain $AdS$ bulk gravity theories, we find that the radial flows of double trace deformations in the boundary effective actions are completely captured by stochastic time evolution with identification of the $AdS$ radial coordinate `$r$' with the stochastic time '$t$' as $r=t$. More precisely, we investigate Langevin dynamics and find an exact relation between radial flow of the double trace couplings and 2-point correlation functions in stochastic quantization. We also show that the radial evolution of double trace deformations in the boundary effective action and the stochastic time evolution of the Fokker-Planck action are the same. We demonstrate this relation with a couple of examples: (minimally coupled)massless scalar fields in $Ad{S}_2$ and U(1) vector fields in $Ad{S}_4$.

1+30 pages, a new subsection is added, references are added

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• Stochastic quantization and holographic Wilsonian renormalization group of massless fermions in AdS
• Stochastic quantization and holographic Wilsonian renormalization group of free massive fermion
• Stochastic quantization and holographic Wilsonian renormalization group of scalar theories with arbitrary mass
• 4-point function from conformally coupled scalar in AdS${}_6$
• Stochastic quantization of a self-interacting nonminimal scalar field in semiclassical gravity
• Transport Coefficients for Holographic Hydrodynamics at Finite Energy Scale
• On holographic Wilsonian renormalization group of massive scalar theory with its self-interactions in AdS
• On Functional and Holographic Renormalization Group Methods in Stochastic Theory of Turbulence
• Stochastic quantization and holographic Wilsonian renormalization group of conformally coupled scalar in AdS${}_4$
• First order formalism of holographic Wilsonian renormalization group: Langevin equation
• Stochastic quantization and holographic Wilsonian renormalization group of scalar theory with generic mass, self-interaction and multiple trace deformation