Momentum-space Langevin dynamics of holographic Wilsonian RG flow: self-interacting massive scalar field theory
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916582497714176 |
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| author | Chae, Ji-seong Oh, Jae-Hyuk |
| author_facet | Chae, Ji-seong Oh, Jae-Hyuk |
| contents | We explore mathematical relationship between holographic Wilsonian renormalization group(HWRG) and stochastic quantization(SQ) motivated by the similarity of the monotonicity in RG flow with Langevin dynamics of non-equilibrium thermodynamics. We look at scalar field theory in AdS space with its generic mass, self-interaction, and boundary deformation in the momentum space. Identifying the stochastic time $t$ with radial coordinate $r$ in AdS, we establish maps between the fictitious time evolution of stochastic multi point correlation function and the radial evolution of multi-trace deformation, which respectively, express the relaxation process of Langevin dynamics and holographic RG flow. We especially consider marginal multi-trace deformation on the AdS boundary which is successfully captured by a Langevin dynamics of SQ. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03841 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Momentum-space Langevin dynamics of holographic Wilsonian RG flow: self-interacting massive scalar field theory Chae, Ji-seong Oh, Jae-Hyuk High Energy Physics - Theory We explore mathematical relationship between holographic Wilsonian renormalization group(HWRG) and stochastic quantization(SQ) motivated by the similarity of the monotonicity in RG flow with Langevin dynamics of non-equilibrium thermodynamics. We look at scalar field theory in AdS space with its generic mass, self-interaction, and boundary deformation in the momentum space. Identifying the stochastic time $t$ with radial coordinate $r$ in AdS, we establish maps between the fictitious time evolution of stochastic multi point correlation function and the radial evolution of multi-trace deformation, which respectively, express the relaxation process of Langevin dynamics and holographic RG flow. We especially consider marginal multi-trace deformation on the AdS boundary which is successfully captured by a Langevin dynamics of SQ. |
| title | Momentum-space Langevin dynamics of holographic Wilsonian RG flow: self-interacting massive scalar field theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2402.03841 |