Stochastic quantization and holographic Wilsonian renormalization group of scalar theory with generic mass, self-interaction and multiple trace deformation

초록

We explore the mathematical relationship between holographic Wilsonian renormalization group(HWRG) and stochastic quantization(SQ) of scalar field theory with its generic mass, self-interaction and n-multiple-trace deformation on the d-dimensional conformal boundary defined in AdSd+1 spacetime. We understand that once we define our Euclidean action, SE as SE≡−2SB, then the stochastic process will reconstruct the holographic Wilsonian renormalization group data via solving Langevin equation and computing stochastic correlation functions. The SB is given by SB=Sct+Sdef, where Sct is the boundary counter term and Sdef is the boundary deformation which gives a boundary condition. In our study, we choose the boundary condition adding (marginal)n-multiple trace deformation to the holographic dual field theory. In this theory, we establish maps bewteen ficticious time, t evolution of stochastic n-point, (2n−2)-point correlation functions and the (AdS)radial, r evolution of n-multiple-trace and (2n−2)-multiple-trace deformations respectively once we take identifications of r=t and between some of constants appearing in both sides.

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