First-order formalism of holographic Wilsonian renormalization group: Langevin equation

We study a mathematical relationship between holographic Wilsonian renormalization group and stochastic quantization framework. extend the original proposal given in arXiv:1209.2242 to interacting theories. The suggests that fictitious time (or time) evolution of 2-point correlation function will be identical radial double-trace operator certain classes models, which are free theories AdS space. gravity models with interactions space, establish map flow multi-trace operators n-point functions. To give precise examples, we extensively conformally coupled scalar theory $$\hbox {AdS}_6$$ . What have found is t dependent 3-point obtained from Langevin equation its Euclidean action being by $$S_E=2I_{os}$$ triple-trace as energy scale r changes once an identification $$t=r$$ made. $$I_{os}$$ on-shell model at boundary. argue this can fully extended multi-point functions each