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Journal of High Energy Physics

, 2018:86 | Cite as

Finite cutoff AdS5 holography and the generalized gradient flow

  • Vasudev ShyamEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

Recently proposed double trace deformations of large N holographic CFTs in four dimensions define a one parameter family of quantum field theories, which are interpreted in the bulk dual as living on successive finite radius hypersurfaces. The transformation of variables that turns the equation defining the deformation of a four dimensional large N CFT by such operators into the expression for the radial ADM Hamiltonian in the bulk is found.

This prescription clarifies the role of various functions of background fields that appear in the flow equation defining the deformed holographic CFT, and also their relationship to the holographic anomaly.

The effect of these deformations can also be seen as triggering a generalized gradient flow for the fields of the induced gravity theory obtained from integrating out the fundamental fields of the holographic CFT. The potential for this gradient flow is found to resemble the two derivative effective action previously derived using holographic renormalization.

Keywords

AdS-CFT Correspondence Renormalization Group Classical Theories of Gravity Gauge-gravity correspondence 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    I. Heemskerk and J. Polchinski, Holographic and Wilsonian Renormalization Groups, JHEP 06 (2011) 031 [arXiv:1010.1264] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    T. Faulkner, H. Liu and M. Rangamani, Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm, JHEP 08 (2011) 051 [arXiv:1010.4036] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  3. [3]
    I. Papadimitriou, Lectures on Holographic Renormalization, Springer Proc. Phys. 176 (2016) 131.CrossRefzbMATHGoogle Scholar
  4. [4]
    S.-S. Lee, Quantum Renormalization Group and Holography, JHEP 01 (2014) 076 [arXiv:1305.3908] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    R.L. Arnowitt, S. Deser and C.W. Misner, The dynamics of general relativity, Gen. Rel. Grav. 40 (2008) 1997 [gr-qc/0405109] [INSPIRE].
  6. [6]
    L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \( T\overline{T} \) , JHEP 04 (2018) 010 [arXiv:1611.03470] [INSPIRE].
  7. [7]
    P. Kraus, J. Liu and D. Marolf, Cutoff AdS 3 versus the \( T\overline{T} \) deformation, JHEP 07 (2018) 027 [arXiv:1801.02714] [INSPIRE].
  8. [8]
    G. Giribet, \( T\overline{T} \) -deformations, AdS/CFT and correlation functions, JHEP 02 (2018) 114 [arXiv:1711.02716] [INSPIRE].
  9. [9]
    M. Asrat, A. Giveon, N. Itzhaki and D. Kutasov, Holography Beyond AdS, Nucl. Phys. B 932 (2018) 241 [arXiv:1711.02690] [INSPIRE].
  10. [10]
    G. Bonelli, N. Doroud and M. Zhu, \( T\overline{T} \) -deformations in closed form, JHEP 06 (2018) 149 [arXiv:1804.10967] [INSPIRE].
  11. [11]
    M. Taylor, \( T\overline{T} \) deformations in general dimensions, arXiv:1805.10287 [INSPIRE].
  12. [12]
    T. Hartman, J. Kruthoff, E. Shaghoulian and A. Tajdini, Holography at finite cutoff with a T 2 deformation,arXiv:1807.11401[INSPIRE].
  13. [13]
    F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].
  14. [14]
    A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo, \( T\overline{T} \) -deformed 2D Quantum Field Theories, JHEP 10 (2016) 112 [arXiv:1608.05534] [INSPIRE].
  15. [15]
    C. Teitelboim, How commutators of constraints reflect the space-time structure, Annals Phys. 79 (1973) 542 [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    I. Papadimitriou, Holographic Renormalization of general dilaton-axion gravity, JHEP 08 (2011) 119 [arXiv:1106.4826] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
  20. [20]
    S. Jackson, R. Pourhasan and H. Verlinde, Geometric RG Flow, arXiv:1312.6914 [INSPIRE].
  21. [21]
    Y. Nakayama, ac test of holography versus quantum renormalization group, Mod. Phys. Lett. A 29 (2014) 1450158 [arXiv:1401.5257] [INSPIRE].
  22. [22]
    H. Osborn, Weyl consistency conditions and a local renormalization group equation for general renormalizable field theories, Nucl. Phys. B 363 (1991) 486 [INSPIRE].
  23. [23]
    E. Kiritsis, W. Li and F. Nitti, Holographic RG flow and the Quantum Effective Action, Fortsch. Phys. 62 (2014) 389 [arXiv:1401.0888] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    S. Farkas and E.J. Martinec, Gravity from the Extension of Spatial Diffeomorphisms, J. Math. Phys. 52 (2011) 062501 [arXiv:1002.4449] [INSPIRE].
  25. [25]
    H. Gomes and V. Shyam, Extending the rigidity of general relativity, J. Math. Phys. 57 (2016) 112503 [arXiv:1608.08236] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    H. Liu and A.A. Tseytlin, D = 4 superYang-Mills, D = 5 gauged supergravity and D = 4 conformal supergravity, Nucl. Phys. B 533 (1998) 88 [hep-th/9804083] [INSPIRE].
  27. [27]
    M. Lüscher, Properties and uses of the Wilson flow in lattice QCD, JHEP 08 (2010) 071 [Erratum ibid. 03 (2014) 092] [arXiv:1006.4518] [INSPIRE].
  28. [28]
    S. Aoki, K. Kikuchi and T. Onogi, Generalized Gradient Flow Equation and Its Applications, PoS(LATTICE2015)305 (2016) [arXiv:1511.06561] [INSPIRE].
  29. [29]
    S. Aoki, J. Balog, T. Onogi and P. Weisz, Flow equation for the large N scalar model and induced geometries, PTEP 2016 (2016) 083B04 [arXiv:1605.02413] [INSPIRE].
  30. [30]
    S. Aoki, J. Balog, T. Onogi and P. Weisz, Flow equation for the scalar model in the large N expansion and its applications, PTEP 2017 (2017) 043B01 [arXiv:1701.00046] [INSPIRE].
  31. [31]
    S. Aoki and S. Yokoyama, AdS geometry from CFT on a general conformally flat manifold, Nucl. Phys. B 933 (2018) 262 [arXiv:1709.07281] [INSPIRE].
  32. [32]
    S. Aoki and S. Yokoyama, Flow equation, conformal symmetry and anti-de Sitter geometry, PTEP 2018 (2018) 031B01 [arXiv:1707.03982] [INSPIRE].
  33. [33]
    S. Aoki, J. Balog and S. Yokoyama, Holographic computation of quantum corrections to the bulk cosmological constant, arXiv:1804.04636 [INSPIRE].
  34. [34]
    V. Shyam, Background independent holographic dual to \( T\overline{T} \) deformed CFT with large central charge in 2 dimensions, JHEP 10 (2017) 108 [arXiv:1707.08118] [INSPIRE].
  35. [35]
    V. Shyam, Connecting holographic Wess-Zumino consistency condition to the holographic anomaly, JHEP 03 (2018) 171 [arXiv:1712.07955] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    W. Donnelly and V. Shyam, Entanglement entropy and \( T\overline{T} \) deformation, Phys. Rev. Lett. 121 (2018) 131602 [arXiv:1806.07444] [INSPIRE].
  37. [37]
    B. Chen, L. Chen and P.-X. Hao, Entanglement entropy in \( T\overline{T} \) -deformed CFT, Phys. Rev. D 98 (2018) 086025 [arXiv:1807.08293] [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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