Advertisement

Journal of High Energy Physics

, 2019:283 | Cite as

Anomalous gravitation and its positivity from entanglement

  • Hongliang JiangEmail author
Open Access
Regular Article - Theoretical Physics
  • 18 Downloads

Abstract

We explore the emergence of gravitation from entanglement in holographic CFTs with gravitational anomalies. More specifically, the holographic correspondence between topologically massive gravity (TMG) with gravitational Chern-Simons term in the 3D bulk and its dual CFT with unbalanced left and right moving central charges on the 2D boundary, is studied from the quantum entanglement perspective. Using the first law of entanglement, we derive the holographic dictionary of the energy-momentum tensor in TMG, including the chiral case with logarithmic mode. Furthermore, we show that the linearized equation of motion of TMG can also be obtained from entanglement using the Wald-Tachikawa covariant phase space formalism. Finally, we identify a quasi-local gravitational energy in the entanglement wedge as the holographic dual of relative entropy in gravitationally anomalous CFTs. The positivity and monotonicity of relative entropy imply that such a gravitational energy should be positive definite and become larger when increasing the size of the entanglement wedge. These constraints from quantum information may be potentially used to discuss the UV inconsistent issues of TMG.

Keywords

AdS-CFT Correspondence Gauge-gravity correspondence Chern-Simons Theories Conformal and W Symmetry 

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]
    G. ’t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
  2. [2]
    L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  4. [4]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    N. Lashkari, M.B. McDermott and M. Van Raamsdonk, Gravitational dynamics from entanglement ‘thermodynamics’, JHEP 04 (2014) 195 [arXiv:1308.3716] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    T. Faulkner, M. Guica, T. Hartman, R.C. Myers and M. Van Raamsdonk, Gravitation from entanglement in holographic CFTs, JHEP 03 (2014) 051 [arXiv:1312.7856] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    T. Faulkner, F.M. Haehl, E. Hijano, O. Parrikar, C. Rabideau and M. Van Raamsdonk, Nonlinear gravity from entanglement in conformal field theories, JHEP 08 (2017) 057 [arXiv:1705.03026] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    F.M. Haehl, E. Hijano, O. Parrikar and C. Rabideau, Higher curvature gravity from entanglement in conformal field theories, Phys. Rev. Lett. 120 (2018) 201602 [arXiv:1712.06620] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    A. Castro, S. Detournay, N. Iqbal and E. Perlmutter, Holographic entanglement entropy and gravitational anomalies, JHEP 07 (2014) 114 [arXiv:1405.2792] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    K. Skenderis, M. Taylor and B.C. van Rees, Topologically massive gravity and the AdS/CFT correspondence, JHEP 09 (2009) 045 [arXiv:0906.4926] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
  14. [14]
    V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
  15. [15]
    Y. Tachikawa, Black hole entropy in the presence of Chern-Simons terms, Class. Quant. Grav. 24 (2007) 737 [hep-th/0611141] [INSPIRE].
  16. [16]
    N. Lashkari, J. Lin, H. Ooguri, B. Stoica and M. Van Raamsdonk, Gravitational positive energy theorems from information inequalities, PTEP 2016 (2016) 12C109 [arXiv:1605.01075] [INSPIRE].
  17. [17]
    P. Hayden, M. Headrick and A. Maloney, Holographic mutual information is monogamous, Phys. Rev. D 87 (2013) 046003 [arXiv:1107.2940] [INSPIRE].
  18. [18]
    A. Maloney, W. Song and A. Strominger, Chiral gravity, log gravity and extremal CFT, Phys. Rev. D 81 (2010) 064007 [arXiv:0903.4573] [INSPIRE].
  19. [19]
    W. Li, W. Song and A. Strominger, Chiral gravity in three dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [INSPIRE].
  20. [20]
    D. Grumiller and N. Johansson, Instability in cosmological topologically massive gravity at the chiral point, JHEP 07 (2008) 134 [arXiv:0805.2610] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    L. Cheng, L.-Y. Hung, S.-N. Liu and H.-Z. Zhou, First law of entanglement entropy in topologically massive gravity, Phys. Rev. D 94 (2016) 064063 [arXiv:1511.03844] [INSPIRE].
  23. [23]
    P. Kraus and F. Larsen, Holographic gravitational anomalies, JHEP 01 (2006) 022 [hep-th/0508218] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    S. Deser, Positive energy of topologically massive gravity, Class. Quant. Grav. 26 (2009) 192001 [arXiv:0907.4135] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    E. Sezgin and Y. Tanii, Witten-Nester energy in topologically massive gravity, Class. Quant. Grav. 26 (2009) 235005 [arXiv:0903.3779] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    E. Witten, A simple proof of the positive energy theorem, Commun. Math. Phys. 80 (1981) 381 [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    S. Banerjee, A. Bhattacharyya, A. Kaviraj, K. Sen and A. Sinha, Constraining gravity using entanglement in AdS/CFT, JHEP 05 (2014) 029 [arXiv:1401.5089] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    L. Apolo, H. Jiang, W. Song and Y. Zhong, Holographic relative entropy beyond AdS/CFT, in preparation.Google Scholar
  29. [29]
    C.G. Callan Jr. and J.A. Harvey, Anomalies and fermion zero modes on strings and domain walls, Nucl. Phys. B 250 (1985) 427 [INSPIRE].
  30. [30]
    T. Azeyanagi, R. Loganayagam and G.S. Ng, Holographic entanglement for Chern-Simons terms, JHEP 02 (2017) 001 [arXiv:1507.02298] [INSPIRE].
  31. [31]
    N. Lashkari, C. Rabideau, P. Sabella-Garnier and M. Van Raamsdonk, Inviolable energy conditions from entanglement inequalities, JHEP 06 (2015) 067 [arXiv:1412.3514] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    A. Castro, D.M. Hofman and N. Iqbal, Entanglement entropy in warped conformal field theories, JHEP 02 (2016) 033 [arXiv:1511.00707] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    H. Jiang, W. Song and Q. Wen, Entanglement entropy in flat holography, JHEP 07 (2017) 142 [arXiv:1706.07552] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Albert Einstein Center for Fundamental Physics, Institute for Theoretical PhysicsUniversity of BernBernSwitzerland

Personalised recommendations