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.
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References
G. ’t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
N. Lashkari, M.B. McDermott and M. Van Raamsdonk, Gravitational dynamics from entanglement ‘thermodynamics’, JHEP 04 (2014) 195 [arXiv:1308.3716] [INSPIRE].
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].
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].
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].
A. Castro, S. Detournay, N. Iqbal and E. Perlmutter, Holographic entanglement entropy and gravitational anomalies, JHEP 07 (2014) 114 [arXiv:1405.2792] [INSPIRE].
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].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
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].
Y. Tachikawa, Black hole entropy in the presence of Chern-Simons terms, Class. Quant. Grav. 24 (2007) 737 [hep-th/0611141] [INSPIRE].
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].
P. Hayden, M. Headrick and A. Maloney, Holographic mutual information is monogamous, Phys. Rev. D 87 (2013) 046003 [arXiv:1107.2940] [INSPIRE].
A. Maloney, W. Song and A. Strominger, Chiral gravity, log gravity and extremal CFT, Phys. Rev. D 81 (2010) 064007 [arXiv:0903.4573] [INSPIRE].
W. Li, W. Song and A. Strominger, Chiral gravity in three dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [INSPIRE].
D. Grumiller and N. Johansson, Instability in cosmological topologically massive gravity at the chiral point, JHEP 07 (2008) 134 [arXiv:0805.2610] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
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].
P. Kraus and F. Larsen, Holographic gravitational anomalies, JHEP 01 (2006) 022 [hep-th/0508218] [INSPIRE].
S. Deser, Positive energy of topologically massive gravity, Class. Quant. Grav. 26 (2009) 192001 [arXiv:0907.4135] [INSPIRE].
E. Sezgin and Y. Tanii, Witten-Nester energy in topologically massive gravity, Class. Quant. Grav. 26 (2009) 235005 [arXiv:0903.3779] [INSPIRE].
E. Witten, A simple proof of the positive energy theorem, Commun. Math. Phys. 80 (1981) 381 [INSPIRE].
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].
L. Apolo, H. Jiang, W. Song and Y. Zhong, Holographic relative entropy beyond AdS/CFT, in preparation.
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].
T. Azeyanagi, R. Loganayagam and G.S. Ng, Holographic entanglement for Chern-Simons terms, JHEP 02 (2017) 001 [arXiv:1507.02298] [INSPIRE].
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].
A. Castro, D.M. Hofman and N. Iqbal, Entanglement entropy in warped conformal field theories, JHEP 02 (2016) 033 [arXiv:1511.00707] [INSPIRE].
H. Jiang, W. Song and Q. Wen, Entanglement entropy in flat holography, JHEP 07 (2017) 142 [arXiv:1706.07552] [INSPIRE].
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ArXiv ePrint: 1906.04142
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Jiang, H. Anomalous gravitation and its positivity from entanglement. J. High Energ. Phys. 2019, 283 (2019). https://doi.org/10.1007/JHEP10(2019)283
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DOI: https://doi.org/10.1007/JHEP10(2019)283