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Sparseness bounds on local operators in holographic CFTd

  • Eric Mefford
  • Edgar Shaghoulian
  • Milind Shyani
Open Access
Regular Article - Theoretical Physics
  • 24 Downloads

Abstract

We use the thermodynamics of anti-de Sitter gravity to derive sparseness bounds on the spectrum of local operators in holographic conformal field theories. The simplest such bound is \( \rho \left(\varDelta \right)\lesssim \exp \left(\frac{2\pi \Delta}{d-1}\right) \) for CFTd. Unlike the case of d = 2, this bound is strong enough to rule out weakly coupled holographic theories. We generalize the bound to include spins Ji and U(1) charge Q, obtaining bounds on ρ, Ji, Q) in d = 3 through 6. All bounds are saturated by black holes at the Hawking-Page transition and vanish beyond the corresponding BPS bound.

Keywords

AdS-CFT Correspondence Black Holes Conformal Field Theory Gaugegravity 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]
    T. Hartman, C.A. Keller and B. Stoica, Universal Spectrum of 2d Conformal Field Theory in the Large c Limit, JHEP 09 (2014) 118 [arXiv:1405.5137] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    N. Benjamin, M.C.N. Cheng, S. Kachru, G.W. Moore and N.M. Paquette, Elliptic Genera and 3d Gravity, Annales Henri Poincaré 17 (2016) 2623 [arXiv:1503.04800] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    P. Kraus, A. Sivaramakrishnan and R. Snively, Black holes from CFT: Universality of correlators at large c, JHEP 08 (2017) 084 [arXiv:1706.00771] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    A. Belin, J. de Boer, J. Kruthoff, B. Michel, E. Shaghoulian and M. Shyani, Universality of sparse d > 2 conformal field theory at large N, JHEP 03 (2017) 067 [arXiv:1610.06186] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    E. Shaghoulian, Emergent gravity from Eguchi-Kawai reduction, JHEP 03 (2017) 011 [arXiv:1611.04189] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn-deconfinement phase transition in weakly coupled large N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    P. Kraus and F. Larsen, Microscopic black hole entropy in theories with higher derivatives, JHEP 09 (2005) 034 [hep-th/0506176] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    T. Nishioka and T. Takayanagi, On Type IIA Penrose Limit and N = 6 Chern-Simons Theories, JHEP 08 (2008) 001 [arXiv:0806.3391] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    K. Landsteiner, String corrections to the Hawking-Page phase transition, Mod. Phys. Lett. A 14 (1999) 379 [hep-th/9901143] [INSPIRE].
  13. [13]
    M. Spradlin and A. Volovich, A pendant for Polya: The one-loop partition function of N = 4 SYM on R × S 3, Nucl. Phys. B 711 (2005) 199 [hep-th/0408178] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  14. [14]
    G. Papathanasiou and M. Spradlin, The Morphology of N = 6 Chern-Simons Theory, JHEP 07 (2009) 036 [arXiv:0903.2548] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    E.P. Verlinde, On the holographic principle in a radiation dominated universe, hep-th/0008140 [INSPIRE].
  16. [16]
    K. Jensen, Chiral anomalies and AdS/CMT in two dimensions, JHEP 01 (2011) 109 [arXiv:1012.4831] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    P. Kraus, Lectures on black holes and the AdS 3 /CFT 2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [INSPIRE].
  18. [18]
    C. Martinez, C. Teitelboim and J. Zanelli, Charged rotating black hole in three space-time dimensions, Phys. Rev. D 61 (2000) 104013 [hep-th/9912259] [INSPIRE].ADSGoogle Scholar
  19. [19]
    M. Bañados, G. Barnich, G. Compere and A. Gomberoff, Three dimensional origin of Godel spacetimes and black holes, Phys. Rev. D 73 (2006) 044006 [hep-th/0512105] [INSPIRE].ADSGoogle Scholar
  20. [20]
    M.M. Caldarelli, G. Cognola and D. Klemm, Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories, Class. Quant. Grav. 17 (2000) 399 [hep-th/9908022] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Holography, thermodynamics and fluctuations of charged AdS black holes, Phys. Rev. D 60 (1999) 104026 [hep-th/9904197] [INSPIRE].ADSMathSciNetGoogle Scholar
  22. [22]
    A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].ADSMathSciNetGoogle Scholar
  23. [23]
    S.W. Hawking, C.J. Hunter and M. Taylor, Rotation and the AdS/CFT correspondence, Phys. Rev. D 59 (1999) 064005 [hep-th/9811056] [INSPIRE].ADSMathSciNetGoogle Scholar
  24. [24]
    G.W. Gibbons, H. Lü, D.N. Page and C.N. Pope, The General Kerr-de Sitter metrics in all dimensions, J. Geom. Phys. 53 (2005) 49 [hep-th/0404008] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    G.W. Gibbons, H. Lü, D.N. Page and C.N. Pope, Rotating black holes in higher dimensions with a cosmological constant, Phys. Rev. Lett. 93 (2004) 171102 [hep-th/0409155] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    V.A. Kostelecky and M.J. Perry, Solitonic black holes in gauged N = 2 supergravity, Phys. Lett. B 371 (1996) 191 [hep-th/9512222] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    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
  28. [28]
    M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, General non-extremal rotating black holes in minimal five-dimensional gauged supergravity, Phys. Rev. Lett. 95 (2005) 161301 [hep-th/0506029] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  30. [30]
    D.D.K. Chow, Charged rotating black holes in six-dimensional gauged supergravity, Class. Quant. Grav. 27 (2010) 065004 [arXiv:0808.2728] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    D.D.K. Chow, Equal charge black holes and seven dimensional gauged supergravity, Class. Quant. Grav. 25 (2008) 175010 [arXiv:0711.1975] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    G.T. Horowitz, J.E. Santos and B. Way, Evidence for an Electrifying Violation of Cosmic Censorship, Class. Quant. Grav. 33 (2016) 195007 [arXiv:1604.06465] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    T. Crisford, G.T. Horowitz and J.E. Santos, Testing the Weak Gravity - Cosmic Censorship Connection, Phys. Rev. D 97 (2018) 066005 [arXiv:1709.07880] [INSPIRE].ADSGoogle Scholar
  34. [34]
    D. Kutasov and F. Larsen, Partition sums and entropy bounds in weakly coupled CFT, JHEP 01 (2001) 001 [hep-th/0009244] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    E. Shaghoulian, Modular forms and a generalized Cardy formula in higher dimensions, Phys. Rev. D 93 (2016) 126005 [arXiv:1508.02728] [INSPIRE].ADSMathSciNetGoogle Scholar
  36. [36]
    E. Shaghoulian, Black hole microstates in AdS, Phys. Rev. D 94 (2016) 104044 [arXiv:1512.06855] [INSPIRE].ADSMathSciNetGoogle Scholar
  37. [37]
    R.-G. Cai, The Cardy-Verlinde formula and AdS black holes, Phys. Rev. D 63 (2001) 124018 [hep-th/0102113] [INSPIRE].ADSMathSciNetGoogle Scholar
  38. [38]
    R.-G. Cai, Y.S. Myung and N. Ohta, Bekenstein bound, holography and brane cosmology in charged black hole background, Class. Quant. Grav. 18 (2001) 5429 [hep-th/0105070] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    R.-G. Cai, L.-M. Cao and D.-W. Pang, Thermodynamics of dual CFTs for Kerr-AdS black holes, Phys. Rev. D 72 (2005) 044009 [hep-th/0505133] [INSPIRE].ADSGoogle Scholar
  40. [40]
    G.W. Gibbons, M.J. Perry and C.N. Pope, Bulk/boundary thermodynamic equivalence and the Bekenstein and cosmic-censorship bounds for rotating charged AdS black holes, Phys. Rev. D 72 (2005) 084028 [hep-th/0506233] [INSPIRE].ADSMathSciNetGoogle Scholar
  41. [41]
    E. Shaghoulian, Modular Invariance of Conformal Field Theory on S 1 × S 3 and Circle Fibrations, Phys. Rev. Lett. 119 (2017) 131601 [arXiv:1612.05257] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  42. [42]
    G.T. Horowitz and E. Shaghoulian, Detachable circles and temperature-inversion dualities for CFT d, JHEP 01 (2018) 135 [arXiv:1709.06084] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  43. [43]
    E. Shaghoulian, Nonlocal operators in CFT, to be published.Google Scholar
  44. [44]
    D. Jafferis, B. Mukhametzhanov and A. Zhiboedov, Conformal Bootstrap At Large Charge, arXiv:1710.11161 [INSPIRE].
  45. [45]
    S. Hellerman, D. Orlando, S. Reffert and M. Watanabe, On the CFT Operator Spectrum at Large Global Charge, JHEP 12 (2015) 071 [arXiv:1505.01537] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  46. [46]
    A. Monin, D. Pirtskhalava, R. Rattazzi and F.K. Seibold, Semiclassics, Goldstone Bosons and CFT data, JHEP 06 (2017) 011 [arXiv:1611.02912] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    S. Hellerman, A Universal Inequality for CFT and Quantum Gravity, JHEP 08 (2011) 130 [arXiv:0902.2790] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    M. Cvetič, H. Lü and C.N. Pope, Gauged six-dimensional supergravity from massive type IIA, Phys. Rev. Lett. 83 (1999) 5226 [hep-th/9906221] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  2. 2.Department of PhysicsCornell UniversityIthacaU.S.A.
  3. 3.Stanford Institute for Theoretical PhysicsStanfordU.S.A.

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