Abstract
We compute the holographic entanglement entropy for the anomaly polynomial TrR 2 in 3+1 dimensions. Using the perturbative method developed for computing entanglement entropy for quantum field theories, we also compute the parity odd contribution to the entanglement entropy of the dual field theory that comes from a background gravitational Chern-Simons term. We find that, in leading order in the perturbation of the background geometry, the two contributions match except for a logarithmic divergent term on the field theory side. We interpret this extra contribution as encoding our ignorance of the source which creates the perturbation of the geometry.
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References
N. Seiberg, Emergent spacetime, in proceedings of 23rd Solvay Conference on Physics: The Quantum Structure of Space and Time, Brussels, Belgium, December 1-3, 2005, hep-th/0601234 [INSPIRE].
R. de Mello Koch and J. Murugan, Emergent Spacetime, in proceedings of Foundations of Space and Time: Reflections on Quantum Gravity, Cape Town, South Africa, August 10-14, 2009, arXiv:0911.4817 [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].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
X. Dong, Holographic Entanglement Entropy for General Higher Derivative Gravity, JHEP 01 (2014) 044 [arXiv:1310.5713] [INSPIRE].
A. Castro, S. Detournay, N. Iqbal and E. Perlmutter, Holographic entanglement entropy and gravitational anomalies, JHEP 07 (2014) 114 [arXiv:1405.2792] [INSPIRE].
J. de Boer, M. Kulaxizi and A. Parnachev, Holographic Entanglement Entropy in Lovelock Gravities, JHEP 07 (2011) 109 [arXiv:1101.5781] [INSPIRE].
L.-Y. Hung, R.C. Myers and M. Smolkin, On Holographic Entanglement Entropy and Higher Curvature Gravity, JHEP 04 (2011) 025 [arXiv:1101.5813] [INSPIRE].
J. Camps, Generalized entropy and higher derivative Gravity, JHEP 03 (2014) 070 [arXiv:1310.6659] [INSPIRE].
R.C. Myers, R. Pourhasan and M. Smolkin, On Spacetime Entanglement, JHEP 06 (2013) 013 [arXiv:1304.2030] [INSPIRE].
A. Bhattacharyya, A. Kaviraj and A. Sinha, Entanglement entropy in higher derivative holography, JHEP 08 (2013) 012 [arXiv:1305.6694] [INSPIRE].
M.R. Mohammadi Mozaffar, A. Mollabashi, M.M. Sheikh-Jabbari and M.H. Vahidinia, Holographic Entanglement Entropy, Field Redefinition Invariance and Higher Derivative Gravity Theories, Phys. Rev. D 94 (2016) 046002 [arXiv:1603.05713] [INSPIRE].
R. Jackiw and S.Y. Pi, Chern-Simons modification of general relativity, Phys. Rev. D 68 (2003) 104012 [gr-qc/0308071] [INSPIRE].
L. Álvarez-Gaumé and E. Witten, Gravitational Anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].
A. Kitaev and J. Preskill, Topological entanglement entropy, Phys. Rev. Lett. 96 (2006) 110404 [hep-th/0510092] [INSPIRE].
S. Deser, M.J. Duff and C.J. Isham, Gravitationally Induced CP Effects, Phys. Lett. B 93 (1980) 419 [INSPIRE].
T. Azeyanagi, R. Loganayagam and G.S. Ng, Holographic Entanglement for Chern-Simons Terms, JHEP 02 (2017) 001 [arXiv:1507.02298] [INSPIRE].
P. Fonda, V. Jejjala and A. Veliz-Osorio, On the Shape of Things: From holography to elastica, arXiv:1611.03462 [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
X. Dong, A. Lewkowycz and M. Rangamani, Deriving covariant holographic entanglement, JHEP 11 (2016) 028 [arXiv:1607.07506] [INSPIRE].
S. Deser, R. Jackiw and G. ’t Hooft, Three-Dimensional Einstein Gravity: Dynamics of Flat Space, Annals Phys. 152 (1984) 220 [INSPIRE].
S. Deser, R. Jackiw and G. ’t Hooft, Physical cosmic strings do not generate closed timelike curves, Phys. Rev. Lett. 68 (1992) 267 [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Topologically Massive Gauge Theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Three-Dimensional Massive Gauge Theories, Phys. Rev. Lett. 48 (1982) 975 [INSPIRE].
W. Fischler and S. Kundu, Membrane paradigm, gravitational Θ-term and gauge/gravity duality, JHEP 04 (2016) 112 [arXiv:1512.01238] [INSPIRE].
V. Rosenhaus and M. Smolkin, Entanglement Entropy: A Perturbative Calculation, JHEP 12 (2014) 179 [arXiv:1403.3733] [INSPIRE].
V. Rosenhaus and M. Smolkin, Entanglement Entropy for Relevant and Geometric Perturbations, JHEP 02 (2015) 015 [arXiv:1410.6530] [INSPIRE].
T.L. Hughes, R.G. Leigh, O. Parrikar and S.T. Ramamurthy, Entanglement entropy and anomaly inflow, Phys. Rev. D 93 (2016) 065059 [arXiv:1509.04969] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Comments on Chern-Simons Contact Terms in Three Dimensions, JHEP 09 (2012) 091 [arXiv:1206.5218] [INSPIRE].
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ArXiv ePrint: 1611.03415
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Ali, T., Haque, S.S. & Murugan, J. Holographic entanglement entropy for gravitational anomaly in four dimensions. J. High Energ. Phys. 2017, 84 (2017). https://doi.org/10.1007/JHEP03(2017)084
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DOI: https://doi.org/10.1007/JHEP03(2017)084