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arXiv · 2308.10010

Stochastic quantization and holographic Wilsonian renormalization group of conformally coupled scalar in AdS$_{4}$

Jun Hyeok Lee·Jae-Hyuk Oh
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Abstract

In this paper, we explore the relationship between holographic Wilsonian renormalization groups and stochastic quantization in conformally coupled scalar theory in AdS$_{4}$. The relationship between these two different frameworks is firstly proposed in arXiv:1209.2242 and tested in various free theories. However, research on the theory with interactions has recently begun. In this paper, we show that the stochastic four-point function obtained by the Langevin equation is completely captured by the holographic quadruple trace deformation when the Euclidean action $S_{E}$ is given by $S_{E}=-2I_{os}$ where $I_{os}$ is the holographic on-shell action in the conformally coupled scalar theory in AdS$_{4},$ together with a condition that the stochastic fictitious time $t$ is also identified with AdS radial variable $r$. We extensively explore a case that the boundary condition on the conformal boundary is Dirichlet boundary condition, and in that case, the stochastic three-point function trivially vanishes. This agrees with that the holographic triple trace deformation vanishes when Dirichlet boundary condition is applied on the conformal boundary.

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Jun Hyeok Lee, Jae-Hyuk Oh. 2023-08-19. Stochastic quantization and holographic Wilsonian renormalization group of conformally coupled scalar in AdS$_{4}$. https://doi.org/10.1007/s40042-023-00926-3

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