First-order formalism of holographic Wilsonian renormalization group: Langevin equationopen access
- Authors
- Oh, Jae-Hyuk
- Issue Date
- Nov-2021
- Publisher
- KOREAN PHYSICAL SOC
- Keywords
- Stochastic quantization; Holographic Wilsonian RG; Langevin equation; Multi-trace operators
- Citation
- JOURNAL OF THE KOREAN PHYSICAL SOCIETY, v.79, no.10, pp.903 - 917
- Indexed
- SCIE
SCOPUS
KCI
- Journal Title
- JOURNAL OF THE KOREAN PHYSICAL SOCIETY
- Volume
- 79
- Number
- 10
- Start Page
- 903
- End Page
- 917
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/140540
- DOI
- 10.1007/s40042-021-00320-x
- ISSN
- 0374-4884
- Abstract
- We study a mathematical relationship between holographic Wilsonian renormalization group and stochastic quantization framework. We extend the original proposal given in arXiv:1209.2242 to interacting theories. The original proposal suggests that fictitious time (or stochastic time) evolution of stochastic 2-point correlation function will be identical to the radial evolution of the double-trace operator of certain classes of holographic models, which are free theories in AdS space. We study holographic gravity models with interactions in AdS space, and establish a map between the holographic renormalization flow of multi-trace operators and stochastic n-point functions. To give precise examples, we extensively study conformally coupled scalar theory in AdS(6). What we have found is that the stochastic time t dependent 3-point function obtained from Langevin equation with its Euclidean action being given by S-E = 2I(os) is identical to holographic renormalization group evolution of holographic triple-trace operator as its energy scale r changes once an identification of t = r is made. I-os is the on-shell action of holographic model of conformally coupled scalar theory at the AdS boundary. We argue that this can be fully extended to mathematical relationship between multi-point functions and multi-trace operators in each framework.
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