Stochastic quantization and holographic Wilsonian renormalization group of conformally coupled scalar in AdS 4

초록

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 SE is given by SE= - 2 Ios where Ios 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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