Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, p-forms

Abstract

We show that the entanglement entropy of D = 4 linearized gravitons across a sphere recently computed by Benedetti and Casini coincides with that obtained using the Kaluza-Klein tower of traceless transverse massive spin-2 fields on S1 × AdS3. The mass of the constant mode on S1 saturates the Brietenholer-Freedman bound in AdS3. This condition also ensures that the entanglement entropy of higher spins determined from partition functions on the hyperbolic cylinder coincides with their recent conjecture. Starting from the action of the 2-form on S1 × AdS5 and fixing gauge, we evaluate the entanglement entropy across a sphere as well as the dimensions of the corresponding twist operator. We demonstrate that the conformal dimensions of the corresponding twist operator agrees with that obtained using the expectation value of the stress tensor on the replica cone. For conformal p-forms in even dimensions it obeys the expected relations with the coefficients determining the 3-point function of the stress tensor of these fields.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    V. Benedetti and H. Casini, Entanglement entropy of linearized gravitons in a sphere, Phys. Rev. D 101 (2020) 045004 [arXiv:1908.01800] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  2. [2]

    W. Donnelly and A.C. Wall, Entanglement entropy of electromagnetic edge modes, Phys. Rev. Lett. 114 (2015) 111603 [arXiv:1412.1895] [INSPIRE].

    ADS  Article  Google Scholar 

  3. [3]

    K.-W. Huang, Central charge and entangled gauge fields, Phys. Rev. D 92 (2015) 025010 [arXiv:1412.2730] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  4. [4]

    W. Donnelly and A.C. Wall, Geometric entropy and edge modes of the electromagnetic field, Phys. Rev. D 94 (2016) 104053 [arXiv:1506.05792] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  5. [5]

    R.M. Soni and S.P. Trivedi, Entanglement entropy in (3 + 1)-d free U(1) gauge theory, JHEP 02 (2017) 101 [arXiv:1608.00353] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  6. [6]

    U. Moitra, R.M. Soni and S.P. Trivedi, Entanglement entropy, relative entropy and duality, JHEP 08 (2019) 059 [arXiv:1811.06986] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  7. [7]

    J.S. Dowker, Note on the entanglement entropy of higher spins in four dimensions, arXiv:1908.04870 [INSPIRE].

  8. [8]

    J.S. Dowker, Arbitrary spin theory in the Einstein universe, Phys. Rev. D 28 (1983) 3013 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  9. [9]

    H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  10. [10]

    E.S. Fradkin and A.A. Tseytlin, One loop effective potential in gauged O(4) supergravity, Nucl. Phys. B 234 (1984) 472 [INSPIRE].

    ADS  Article  Google Scholar 

  11. [11]

    J.R. David, M.R. Gaberdiel and R. Gopakumar, The heat kernel on AdS3 and its applications, JHEP 04 (2010) 125 [arXiv:0911.5085] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  12. [12]

    M.R. Gaberdiel, R. Gopakumar and A. Saha, Quantum W -symmetry in AdS3, JHEP 02 (2011) 004 [arXiv:1009.6087] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  13. [13]

    P. Candelas and D. Deutsch, On the vacuum stress induced by uniform acceleration or supporting the ether, Proc. Roy. Soc. Lond. A 354 (1977) 79.

    ADS  MathSciNet  Article  Google Scholar 

  14. [14]

    L.-Y. Hung, R.C. Myers and M. Smolkin, Twist operators in higher dimensions, JHEP 10 (2014) 178 [arXiv:1407.6429] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  15. [15]

    D. Anninos, F. Denef, Y.T.A. Law and Z. Sun, Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions, arXiv:2009.12464 [INSPIRE].

  16. [16]

    L.-Y. Hung, R.C. Myers, M. Smolkin and A. Yale, Holographic calculations of Renyi entropy, JHEP 12 (2011) 047 [arXiv:1110.1084] [INSPIRE].

    ADS  Article  Google Scholar 

  17. [17]

    H. Casini and M. Huerta, Entanglement entropy for the n-sphere, Phys. Lett. B 694 (2011) 167 [arXiv:1007.1813] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  18. [18]

    C.P. Herzog and T. Nishioka, The edge of entanglement: getting the boundary right for non-minimally coupled scalar fields, JHEP 12 (2016) 138 [arXiv:1610.02261] [INSPIRE].

    ADS  Article  Google Scholar 

  19. [19]

    I.R. Klebanov, S.S. Pufu, S. Sachdev and B.R. Safdi, Renyi entropies for free field theories, JHEP 04 (2012) 074 [arXiv:1111.6290] [INSPIRE].

    ADS  Article  Google Scholar 

  20. [20]

    R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. 35 (1994) 4217 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  21. [21]

    J.S. Dowker, Vacuum averages for arbitrary spin around a cosmic string, Phys. Rev. D 36 (1987) 3742 [INSPIRE].

    ADS  Article  Google Scholar 

  22. [22]

    J.S. Dowker, Entanglement entropy for even spheres, arXiv:1009.3854 [INSPIRE].

  23. [23]

    C. Eling, Y. Oz and S. Theisen, Entanglement and thermal entropy of gauge fields, JHEP 11 (2013) 019 [arXiv:1308.4964] [INSPIRE].

    ADS  Article  Google Scholar 

  24. [24]

    H. Casini and M. Huerta, Entanglement entropy of a Maxwell field on the sphere, Phys. Rev. D 93 (2016) 105031 [arXiv:1512.06182] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  25. [25]

    H. Casini, M. Huerta, J.M. Magán and D. Pontello, Logarithmic coefficient of the entanglement entropy of a Maxwell field, Phys. Rev. D 101 (2020) 065020 [arXiv:1911.00529] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  26. [26]

    R. Gopakumar, R.K. Gupta and S. Lal, The heat kernel on AdS, JHEP 11 (2011) 010 [arXiv:1103.3627] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  27. [27]

    H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  28. [28]

    J.S. Dowker, Renyi entropy and CT for p-forms on even spheres, arXiv:1706.04574 [INSPIRE].

  29. [29]

    J. Nian and Y. Zhou, Rényi entropy of a free (2, 0) tensor multiplet and its supersymmetric counterpart, Phys. Rev. D 93 (2016) 125010 [arXiv:1511.00313] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  30. [30]

    R. Camporesi and A. Higuchi, The Plancherel measure for p-forms in real hyperbolic spaces, J. Geom. Phys. 15 (1994) 57.

    ADS  MathSciNet  Article  Google Scholar 

  31. [31]

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

    ADS  MathSciNet  Article  Google Scholar 

  32. [32]

    M. Nozaki, T. Numasawa and T. Takayanagi, Quantum entanglement of local operators in conformal field theories, Phys. Rev. Lett. 112 (2014) 111602 [arXiv:1401.0539] [INSPIRE].

    ADS  Article  Google Scholar 

  33. [33]

    J. Lee, A. Lewkowycz, E. Perlmutter and B.R. Safdi, Rényi entropy, stationarity, and entanglement of the conformal scalar, JHEP 03 (2015) 075 [arXiv:1407.7816] [INSPIRE].

    ADS  Article  Google Scholar 

  34. [34]

    A. Buchel, J. Escobedo, R.C. Myers, M.F. Paulos, A. Sinha and M. Smolkin, Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [INSPIRE].

    ADS  Article  Google Scholar 

  35. [35]

    I.V. Tyutin and M.A. Vasiliev, Lagrangian formulation of irreducible massive fields of arbitrary spin in (2+1)-dimensions, Teor. Mat. Fiz. 113N1 (1997) 45 [hep-th/9704132] [INSPIRE].

  36. [36]

    S. Datta and J.R. David, Higher spin quasinormal modes and one-loop determinants in the BTZ black hole, JHEP 03 (2012) 079 [arXiv:1112.4619] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  37. [37]

    M. Beccaria and A.A. Tseytlin, CT for conformal higher spin fields from partition function on conically deformed sphere, JHEP 09 (2017) 123 [arXiv:1707.02456] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  38. [38]

    R.R. Metsaev, Massive totally symmetric fields in AdSd, Phys. Lett. B 590 (2004) 95 [hep-th/0312297] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  39. [39]

    I.L. Buchbinder, V.A. Krykhtin and P.M. Lavrov, Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space, Nucl. Phys. B 762 (2007) 344 [hep-th/0608005] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  40. [40]

    P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Justin R. David.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 2005.08402

Rights and permissions

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.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

David, J.R., Mukherjee, J. Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, p-forms. J. High Energ. Phys. 2021, 202 (2021). https://doi.org/10.1007/JHEP01(2021)202

Download citation

Keywords

  • Conformal Field Theory
  • Field Theories in Higher Dimensions
  • Higher Spin Gravity