Skip to main content
SpringerLink
Log in

Holographic Wilsonian RG flow and sliding membrane paradigm

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We study the relations between two different approaches to the holographic Renormalization Group (RG) flow at the dual gravity level: One is the radial evolution of the classical equation of motion and the other is the flow equation given by the holographic Wilsonian RG coming from the cut off independence. Apparently, the two flows look different. We give general proofs that the two flows are actually equivalent. The role of the momentum continuity (MC) is essential. We show that MC together with cut off independence gives the evolution equation of the boundary values. Equivalence of conductivity flows in two paradigm has been shown as an explicit example. We also get the connecting formula of Green functions and AC conductivity at arbitrary slice in terms of its value at horizon for various geometry backgrounds.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].

    Article  MathSciNet  MATH  Google Scholar 

  2. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  3. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].

    MathSciNet  MATH  Google Scholar 

  4. T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, arXiv:0907.2694 [SPIRES].

  5. T. Hartman, W. Song and A. Strominger, The Kerr-Fermi sea, arXiv:0912.4265 [SPIRES].

  6. T. Faulkner and J. Polchinski, Semi-holographic Fermi liquids, arXiv:1001.5049 [SPIRES].

  7. V. Balasubramanian, P. Kraus, A.E. Lawrence and S.P. Trivedi, Holographic probes of Anti-de Sitter space-times, Phys. Rev. D 59 (1999) 104021 [hep-th/9808017] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  8. E.T. Akhmedov, A remark on the AdS/CFT correspondence and the renormalization group flow, Phys. Lett. B 442 (1998) 152 [hep-th/9806217] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  9. J. de Boer, E.P. Verlinde and H.L. Verlinde, On the holographic renormalization group, JHEP 08 (2000) 003 [hep-th/9912012] [SPIRES].

    Article  Google Scholar 

  10. L. Susskind and E. Witten, The holographic bound in Anti-de Sitter space, hep-th/9805114 [SPIRES].

  11. K.G. Wilson and J.B. Kogut, The renormalization group and the ϵ-expansion, Phys. Rept. 12 (1974) 75 [SPIRES].

    Article  ADS  Google Scholar 

  12. K.G. Wilson, The renormalization group and critical phenomena, Rev. Mod. Phys. 55 (1983) 583 [SPIRES].

    Article  ADS  Google Scholar 

  13. F.J. Wegner and A. Houghton, Renormalization group equation for critical phenomena, Phys. Rev. A8 (1973) 401 [SPIRES].

    ADS  Google Scholar 

  14. J. Polchinski, Renormalization and effective lagrangians, Nucl. Phys. B 231 (1984) 269 [SPIRES].

    Article  ADS  Google Scholar 

  15. I. Heemskerk and J. Polchinski, Holographic and Wilsonian renormalization groups, arXiv:1010.1264 [SPIRES].

  16. T. Faulkner, H. Liu and M. Rangamani, Integrating out geometry: holographic Wilsonian RG and the membrane paradigm, arXiv:1010.4036 [SPIRES].

  17. I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Wilsonian approach to fluid/gravity duality, JHEP 03 (2011) 141 [arXiv:1006.1902] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  18. N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [SPIRES].

    ADS  Google Scholar 

  19. G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  21. D. Nickel and D.T. Son, Deconstructing holographic liquids, arXiv:1009.3094 [SPIRES].

  22. D.T. Son and A.O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  23. L. Vecchi, Multitrace deformations, Gamow states and stability of AdS/CFT, JHEP 04 (2011) 056 [arXiv:1005.4921] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  24. E. Witten, Multi-trace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [SPIRES].

  25. M. Berkooz, A. Sever and A. Shomer, Double-trace deformations, boundary conditions and spacetime singularities, JHEP 05 (2002) 034 [hep-th/0112264] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  26. W. Mueck, An improved correspondence formula for AdS/CFT with multi-trace operators, Phys. Lett. B 531 (2002) 301 [hep-th/0201100] [SPIRES].

    ADS  Google Scholar 

  27. P. Minces, Multi-trace operators and the generalized AdS/CFT prescription, Phys. Rev. D 68 (2003) 024027 [hep-th/0201172] [SPIRES].

    ADS  Google Scholar 

  28. A. Sever and A. Shomer, A note on multi-trace deformations and AdS/CFT, JHEP 07 (2002) 027 [hep-th/0203168] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  29. M. Li, A note on relation between holographic RG equation and Polchinski’s RG equation, Nucl. Phys. B 579 (2000) 525 [hep-th/0001193] [SPIRES].

    Article  ADS  Google Scholar 

  30. A.C. Petkou, Boundary multi-trace deformations and OPEs in AdS/CFT correspondence, JHEP 06 (2002) 009 [hep-th/0201258] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  31. E.T. Akhmedov, Notes on multi-trace operators and holographic renormalization group, hep-th/0202055 [SPIRES].

  32. E. Ayon-Beato, A. Garbarz, G. Giribet and M. Hassaine, Analytic Lifshitz black holes in higher dimensions, JHEP 04 (2010) 030 [arXiv:1001.2361] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Hanyang University, Seoul, 133–791, Korea

    Sang-Jin Sin

  2. Center for Quantum Spacetime, Sogang University, Seoul, 121–742, Korea

    Yang Zhou

Authors
  1. Sang-Jin Sin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yang Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yang Zhou.

Additional information

ArXiv ePrint:1102.4477

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sin, SJ., Zhou, Y. Holographic Wilsonian RG flow and sliding membrane paradigm. J. High Energ. Phys. 2011, 30 (2011). https://doi.org/10.1007/JHEP05(2011)030

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP05(2011)030

Keywords

Search

Navigation