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Notes on the Exact RG equation and the Wheeler-DeWitt equation

Published 25 Feb 2024 in hep-th | (2402.16100v1)

Abstract: In this note, in the context of the AdS/CFT correspondence, the holographic derivation of the Wilsonian effective action is proposed. Then, the exact RG equation in the boundary theory is derived from the Wheeler-DeWitt equation of the bulk, following the suggestion of arXiv:hep-th/9912012,arXiv:hep-th/9912018, and arXiv:1010.1264. The relationship between the exact RG and Stochastic Quantization is briefly discussed.

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References (46)
  1. J. de Boer, E. P. Verlinde and H. L. Verlinde, “On the holographic renormalization group,” JHEP 0008 (2000) 003 [arXiv:hep-th/9912012].
  2. E. P. Verlinde and H. L. Verlinde, “RG-flow, gravity and the cosmological constant,” JHEP 0005, 034 (2000) [arXiv:hep-th/9912018].
  3. I. Heemskerk and J. Polchinski, “Holographic and Wilsonian Renormalization Groups,” arXiv:1010.1264 [hep-th].
  4. G. Parisi and Y. s. Wu, “Perturbation Theory Without Gauge Fixing,” Sci. Sin.  24, 483 (1981).
  5. P.H.Damgaard and H.Huffel, “STOCHASTIC QUANTIZATION,” SINGAPORE, SINGAPORE: WORLD SCIENTIFIC (1988) 496p,
  6. M. Fukuma, S. Matsuura and T. Sakai, “Holographic renormalization group,” Prog. Theor. Phys.  109, 489 (2003) [arXiv:hep-th/0212314].
  7. T. R. Morris, “The Exact renormalization group and approximate solutions,” Int. J. Mod. Phys.  A 9, 2411 (1994) [arXiv:hep-ph/9308265].
  8. T. R. Morris, “A manifestly gauge invariant exact renormalization group,” arXiv:hep-th/9810104.
  9. J. I. Latorre and T. R. Morris, “Exact scheme independence,” JHEP 0011, 004 (2000) [arXiv:hep-th/0008123].
  10. O. J. Rosten, “Fundamentals of the Exact Renormalization Group,” arXiv:1003.1366 [hep-th].
  11. I. R. Klebanov and E. Witten, “AdS/CFT correspondence and symmetry breaking,” Nucl. Phys.  B 556, 89 (1999) [arXiv:hep-th/9905104].
  12. W. Mueck and K. S. Viswanathan, “Regular and irregular boundary conditions in the AdS/CFT correspondence,” Phys. Rev.  D 60, 081901 (1999) [arXiv:hep-th/9906155].
  13. E. Witten, “Multi-trace operators, boundary conditions, and AdS/CFT correspondence,” arXiv:hep-th/0112258.
  14. E. Witten, “SL(2,Z) action on three-dimensional conformal field theories with Abelian symmetry,” arXiv:hep-th/0307041.
  15. T. Faulkner, H. Liu, M. Rangamani, “Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm,” [arXiv:1010.4036 [hep-th]].
  16. O. Aharony, D. Marolf and M. Rangamani, “Conformal field theories in anti-de Sitter space,” JHEP 1102, 041 (2011) [arXiv:1011.6144 [hep-th]].
  17. D. Marolf and S. F. Ross, “Boundary conditions and new dualities: Vector fields in AdS/CFT,” JHEP 0611, 085 (2006) [arXiv:hep-th/0606113].
  18. D. T. Son, D. Teaney, “Thermal Noise and Stochastic Strings in AdS/CFT,” JHEP 0907, 021 (2009). [arXiv:0901.2338 [hep-th]].
  19. J. Polchinski, “Renormalization And Effective Lagrangians,” Nucl. Phys.  B 231, 269 (1984).
  20. G. Lifschytz, S. D. Mathur and M. Ortiz, “A Note on the semiclassical approximation in quantum gravity,” Phys. Rev.  D 53, 766 (1996) [arXiv:gr-qc/9412040].
  21. T. Nishioka, “Horava-Lifshitz Holography,” Class. Quant. Grav.  26, 242001 (2009) [arXiv:0905.0473 [hep-th]].
  22. D. Orlando and S. Reffert, “On the Renormalizability of Horava-Lifshitz-type Gravities,” Class. Quant. Grav.  26, 155021 (2009) [arXiv:0905.0301 [hep-th]].
  23. L. G. Yaffe, “Large N Limits As Classical Mechanics,” Rev. Mod. Phys.  54, 407 (1982).
  24. J. L. F. Barbon, “Multitrace AdS/CFT and master field dynamics,” Phys. Lett.  B 543, 283 (2002) [arXiv:hep-th/0206207].
  25. Y. Makeenko, “Large-N gauge theories,” arXiv:hep-th/0001047.
  26. J. C. Gaite, “Stochastic formulation of the renormalization group: Supersymmetric structure and topology of the space of couplings,” J. Phys. A 37, 10409 (2004) [arXiv:hep-th/0404212].
  27. S. Hirano, “Exact renormalization group and loop equation,” Phys. Rev.  D 61, 125011 (2000) [arXiv:hep-th/9910256].
  28. G. Lifschytz and V. Periwal, “Schwinger-Dyson = Wheeler-DeWitt: Gauge theory observables as bulk operators,” JHEP 0004, 026 (2000) [arXiv:hep-th/0003179].
  29. T. Jacobson, “Thermodynamics of space-time: The Einstein equation of state,” Phys. Rev. Lett.  75, 1260 (1995) [arXiv:gr-qc/9504004].
  30. E. P. Verlinde, “On the Origin of Gravity and the Laws of Newton,” arXiv:1001.0785 [hep-th].
  31. S. J. Sin and Y. Zhou, “Holographic Wilsonian RG Flow and Sliding Membrane Paradigm,” JHEP 05, 030 (2011) doi:10.1007/JHEP05(2011)030 [arXiv:1102.4477 [hep-th]].
  32. V. Balasubramanian, M. Guica and A. Lawrence, “Holographic Interpretations of the Renormalization Group,” JHEP 01, 115 (2013) doi:10.1007/JHEP01(2013)115 [arXiv:1211.1729 [hep-th]].
  33. R. G. Leigh, O. Parrikar and A. B. Weiss, “Exact renormalization group and higher-spin holography,” Phys. Rev. D 91, no.2, 026002 (2015) doi:10.1103/PhysRevD.91.026002 [arXiv:1407.4574 [hep-th]].
  34. B. Sathiapalan and H. Sonoda, “A Holographic form for Wilson’s RG,” Nucl. Phys. B 924, 603-642 (2017) doi:10.1016/j.nuclphysb.2017.09.018 [arXiv:1706.03371 [hep-th]].
  35. B. Sathiapalan and H. Sonoda, “Holographic Wilson’s RG,” Nucl. Phys. B 948, 114767 (2019) doi:10.1016/j.nuclphysb.2019.114767 [arXiv:1902.02486 [hep-th]].
  36. B. Sathiapalan, “Holographic RG and Exact RG in O(N) Model,” Nucl. Phys. B 959, 115142 (2020) doi:10.1016/j.nuclphysb.2020.115142 [arXiv:2005.10412 [hep-th]].
  37. P. Dharanipragada, S. Dutta and B. Sathiapalan, “Bulk gauge fields and holographic RG from exact RG,” JHEP 23, 174 (2020) doi:10.1007/JHEP02(2023)174 [arXiv:2201.06240 [hep-th]].
  38. P. Dharanipragada, S. Dutta and B. Sathiapalan, “Aspects of the map from exact RG to holographic RG in AdS and dS,” Mod. Phys. Lett. A 37, no.37n38, 2250235 (2022) doi:10.1142/S0217732322502352 [arXiv:2301.13605 [hep-th]].
  39. P. Dharanipragada and B. Sathiapalan, “Holographic RG from ERG: Locality and General Coordinate Invariance in the Bulk,” [arXiv:2306.07442 [hep-th]].
  40. D. S. Mansi, A. Mauri and A. C. Petkou, “Stochastic Quantization and AdS/CFT,” Phys. Lett. B 685, 215-221 (2010) doi:10.1016/j.physletb.2010.01.033 [arXiv:0912.2105 [hep-th]].
  41. J. H. Oh and D. P. Jatkar, “Stochastic quantization and holographic Wilsonian renormalization group,” JHEP 11, 144 (2012) doi:10.1007/JHEP11(2012)144 [arXiv:1209.2242 [hep-th]].
  42. D. P. Jatkar and J. H. Oh, “Stochastic quantization of conformally coupled scalar in AdS,” JHEP 10, 170 (2013) doi:10.1007/JHEP10(2013)170 [arXiv:1305.2008 [hep-th]].
  43. J. H. Oh, “First-order formalism of holographic Wilsonian renormalization group: Langevin equation,” J. Korean Phys. Soc. 79, no.10, 903-917 (2021) doi:10.1007/s40042-021-00320-x [arXiv:2110.05013 [hep-th]].
  44. G. Kim, J. s. Chae, W. Shin and J. H. Oh, “Stochastic quantization and holographic Wilsonian renormalization group of scalar theory with generic mass, self-interaction and multiple trace deformation,” Int. J. Mod. Phys. A 38, no.21, 2350114 (2023) doi:10.1142/S0217751X23501142 [arXiv:2305.18920 [hep-th]].
  45. J. H. Lee and J. H. Oh, “Stochastic quantization and holographic Wilsonian renormalization group of conformally coupled scalar in AdS44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT,” J. Korean Phys. Soc. 83, no.9, 665-674 (2023) doi:10.1007/s40042-023-00926-3 [arXiv:2308.10010 [hep-th]].
  46. Y. Hatta and T. Kunihiro, “Renormalization group method applied to kinetic equations: Roles of initial values and time,” Annals Phys. 298, 24-57 (2002) doi:10.1006/aphy.2002.6234 [arXiv:hep-th/0108159 [hep-th]].
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