Stochastic quantization and holographic Wilsonian renormalization group of scalar theories with arbitrary mass

Abstract

We have studied a mathematical relationship between holographic Wilsonian renormalization group(HWRG) and stochastic quantization(SQ) of scalar field with arbitrary mass in AdS spacetime. In the stochastic theory, the field is described by an equation with a form of harmonic oscillator with time dependent frequency and its Euclidean action also shows explicit time dependent kernel in it. We have obtained the stochastic 2-point correlation function and demonstrate that it reproduces the radial evolution of the double trace operator correctly via the suggested relation given in arXiv:1209.2242. Moreover, we justify our stochastic procedure with time dependent kernel by showing that it can be mapped to a new stochastic frame with a standard kernel without time dependence. Finally, we consider more general boundary conditions for the stochastic field to reproduce the radial evolution of the holographic boundary effective action when alternative quantization is allowed. We extensively study the Neumann boundary condition case and confirm that even in this case, the relation between HWRG and SQ is precisely hold.

1+18 pages, a new section is added, typo corrected

References in corpus (5)

• Relating Field Theories via Stochastic Quantization
• Stochastic quantization and holographic Wilsonian renormalization group
• Boundary conditions for SU(2) Yang-Mills on $Ad{S}_4$
• Stochastic quantization and holographic Wilsonian renormalization group of massless fermions in AdS
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Cited by in corpus (5)

• 4-point function from conformally coupled scalar in AdS${}_6$
• On holographic Wilsonian renormalization group of massive scalar theory with its self-interactions in AdS
• Stochastic quantization and holographic Wilsonian renormalization group of conformally coupled scalar in AdS${}_4$
• Stochastic quantization and holographic Wilsonian renormalization group of scalar theory with generic mass, self-interaction and multiple trace deformation
• First order formalism of holographic Wilsonian renormalization group: Langevin equation