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

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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 first 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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Notes

  1. The authors consider a more general boundary condition on AdS boundary and its stochastic frame but they discuss the issues only in zero boundary momenta case [17].

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Acknowledgements

J.H.O thanks his W.J. and Y.J. and he thanks God. This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No.2021R1F1A1047930).

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  1. Department of Physics, Hanyang University, Seoul, 04763, Korea

    Jun Hyeok Lee & Jae-Hyuk Oh

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  1. Jun Hyeok Lee
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Correspondence to Jae-Hyuk Oh.

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Lee, J.H., Oh, JH. Stochastic quantization and holographic Wilsonian renormalization group of conformally coupled scalar in AdS\(_{4}\). J. Korean Phys. Soc. 83, 665–674 (2023). https://doi.org/10.1007/s40042-023-00926-3

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