Abstract
We initiate a systematic study of entanglement and Rényi entropies in the presence of gauge and gravitational anomalies in even-dimensional quantum field theories. We argue that the mixed and gravitational anomalies are sensitive to boosts and obtain a closed form expression for their behavior under such transformations. Explicit constructions exhibiting the dependence of entanglement entropy on boosts is provided for theories on spacetimes with non-trivial magnetic fluxes and (or) non-vanishing Pontryagin classes.
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References
A. Bilal, Lectures on Anomalies, arXiv:0802.0634 [INSPIRE].
J.A. Harvey, TASI 2003 lectures on anomalies, hep-th/0509097 [INSPIRE].
R.A. Bertlmann, International Series of Monographs on Physics. Book 91: Anomalies in Quantum Field Theory, Clarendon Press, Oxford U.K. (2001).
J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].
D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
Y. Neiman and Y. Oz, Relativistic Hydrodynamics with General Anomalous Charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational Anomaly and Transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].
K. Landsteiner, E. Megias, L. Melgar and F. Pena-Benitez, Holographic Gravitational Anomaly and Chiral Vortical Effect, JHEP 09 (2011) 121 [arXiv:1107.0368] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Thermodynamics, gravitational anomalies and cones, JHEP 02 (2013) 088 [arXiv:1207.5824] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Anomaly inflow and thermal equilibrium, JHEP 05 (2014) 134 [arXiv:1310.7024] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Chern-Simons terms from thermal circles and anomalies, JHEP 05 (2014) 110 [arXiv:1311.2935] [INSPIRE].
D.E. Kharzeev, L.D. McLerran and H.J. Warringa, The Effects of topological charge change in heavy ion collisions: ’Event by event P and CP-violation’, Nucl. Phys. A 803 (2008) 227 [arXiv:0711.0950] [INSPIRE].
D.E. Kharzeev, The Chiral Magnetic Effect and Anomaly-Induced Transport, Prog. Part. Nucl. Phys. 75 (2014) 133 [arXiv:1312.3348] [INSPIRE].
D.E. Kharzeev, Topology, magnetic field and strongly interacting matter, Ann. Rev. Nucl. Part. Sci. 65 (2015) 193 [arXiv:1501.01336] [INSPIRE].
D.T. Son and B.Z. Spivak, Chiral Anomaly and Classical Negative Magnetoresistance of Weyl Metals, Phys. Rev. B 88 (2013) 104412 [arXiv:1206.1627] [INSPIRE].
K. Landsteiner, Anomalous transport of Weyl fermions in Weyl semimetals, Phys. Rev. B 89 (2014) 075124 [arXiv:1306.4932] [INSPIRE].
Q. Li et al., Observation of the chiral magnetic effect in ZrTe5, arXiv:1412.6543 [INSPIRE].
C. Zhang et al., Observation of the Adler-Bell-Jackiw chiral anomaly in a Weyl semimetal, arXiv:1503.02630 [INSPIRE].
A. Ohnishi and N. Yamamoto, Magnetars and the Chiral Plasma Instabilities, arXiv:1402.4760 [INSPIRE].
M. Kaminski, C.F. Uhlemann, M. Bleicher and J. Schaffner-Bielich, Anomalous hydrodynamics kicks neutron stars, arXiv:1410.3833 [INSPIRE].
E. Shaverin and A. Yarom, An anomalous propulsion mechanism, arXiv:1411.5581 [INSPIRE].
A.V. Sadofyev and M.V. Isachenkov, The Chiral magnetic effect in hydrodynamical approach, Phys. Lett. B 697 (2011) 404 [arXiv:1010.1550] [INSPIRE].
A.V. Sadofyev, V.I. Shevchenko and V.I. Zakharov, Notes on chiral hydrodynamics within effective theory approach, Phys. Rev. D 83 (2011) 105025 [arXiv:1012.1958] [INSPIRE].
R. Banerjee, P. Chakraborty, S. Dey, B.R. Majhi and A.K. Mitra, Two dimensional hydrodynamics with gauge and gravitational anomalies, Phys. Rev. D 89 (2014) 104013 [arXiv:1307.1313] [INSPIRE].
B.R. Majhi, Connection between response parameter and anomaly coefficient in two dimensional anomalous fluid, JHEP 03 (2014) 001 [arXiv:1401.1074] [INSPIRE].
B.R. Majhi, Vacuum condition and the relation between response parameter and anomaly coefficient in (1 + 3) dimensions, JHEP 08 (2014) 045 [arXiv:1405.4634] [INSPIRE].
S.M. Hosseini and A. Veliz-Osorio, Gravitational anomalies, entanglement entropy and flat-space holography, Phys. Rev. D 93 (2016) 046005 [arXiv:1507.06625] [INSPIRE].
J.-R. Sun, Note on Chern-Simons Term Correction to Holographic Entanglement Entropy, JHEP 05 (2009) 061 [arXiv:0810.0967] [INSPIRE].
A.C. Wall, Testing the Generalized Second Law in 1+1 dimensional Conformal Vacua: An Argument for the Causal Horizon, Phys. Rev. D 85 (2012) 024015 [arXiv:1105.3520] [INSPIRE].
A. Castro, S. Detournay, N. Iqbal and E. Perlmutter, Holographic entanglement entropy and gravitational anomalies, JHEP 07 (2014) 114 [arXiv:1405.2792] [INSPIRE].
W.-z. Guo and R.-x. Miao, Entropy for gravitational Chern-Simons terms by squashed cone method, arXiv:1506.08397 [INSPIRE].
T. Azeyanagi, R. Loganayagam and G.S. Ng, Holographic Entanglement for Chern-Simons Terms, arXiv:1507.02298 [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. (2004) P06002 [hep-th/0405152] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
A. Belin, A. Maloney and S. Matsuura, Holographic Phases of Renyi Entropies, JHEP 12 (2013) 050 [arXiv:1306.2640] [INSPIRE].
J. Camps and W.R. Kelly, Generalized gravitational entropy without replica symmetry, JHEP 03 (2015) 061 [arXiv:1412.4093] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
M.F. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and Riemannian Geometry. I, Math. Proc. Cambridge 77 (1975) 43.
M.F. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and Riemannian Geometry. II, Math. Proc. Cambridge 78 (1975) 405.
M.F. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and Riemannian Geometry. III, Math. Proc. Cambridge 79 (1976) 71.
N. Iqbal and A.C. Wall, Anomalies of the Entanglement Entropy in Chiral Theories, arXiv:1509.04325 [INSPIRE].
T.L. Hughes, R.G. Leigh, O. Parrikar and S.T. Ramamurthy, Entanglement Entropy & Anomaly Inflow, arXiv:1509.04969 [INSPIRE].
C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys. B 424 (1994) 443 [hep-th/9403108] [INSPIRE].
S.N. Solodukhin, Entanglement entropy, conformal invariance and extrinsic geometry, Phys. Lett. B 665 (2008) 305 [arXiv:0802.3117] [INSPIRE].
R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
D.V. Fursaev, A. Patrushev and S.N. Solodukhin, Distributional Geometry of Squashed Cones, Phys. Rev. D 88 (2013) 044054 [arXiv:1306.4000] [INSPIRE].
W.A. Bardeen and B. Zumino, Consistent and Covariant Anomalies in Gauge and Gravitational Theories, Nucl. Phys. B 244 (1984) 421 [INSPIRE].
K. Jensen, P. Kovtun and A. Ritz, Chiral conductivities and effective field theory, JHEP 10 (2013) 186 [arXiv:1307.3234] [INSPIRE].
D.V. Fursaev and S.N. Solodukhin, On the description of the Riemannian geometry in the presence of conical defects, Phys. Rev. D 52 (1995) 2133 [hep-th/9501127] [INSPIRE].
W.S. Massey et al., Non-existence of almost-complex structures on quaternionic projective spaces, Pacific J. Math. 12 (1962) 1379.
J.L. Cardy, O.A. Castro-Alvaredo and B. Doyon, Form factors of branch-point twist fields in quantum integrable models and entanglement entropy, J. Statist. Phys. 130 (2008) 129 [arXiv:0706.3384] [INSPIRE].
O. Lunin and S.D. Mathur, Correlation functions for M N /S N orbifolds, Commun. Math. Phys. 219 (2001) 399 [hep-th/0006196] [INSPIRE].
M. Valle, Hydrodynamics in 1 + 1 dimensions with gravitational anomalies, JHEP 08 (2012) 113 [arXiv:1206.1538] [INSPIRE].
D.S. Hwang, Gauge and Gravitational Anomalies in Two-dimensions, Phys. Rev. D 35 (1987) 1268 [INSPIRE].
K. Ohmori and Y. Tachikawa, Physics at the entangling surface, J. Stat. Mech. 1504 (2015) P04010 [arXiv:1406.4167] [INSPIRE].
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].
S.N. Solodukhin, Holography with gravitational Chern-Simons, Phys. Rev. D 74 (2006) 024015 [hep-th/0509148] [INSPIRE].
S.N. Solodukhin, Holographic description of gravitational anomalies, JHEP 07 (2006) 003 [hep-th/0512216] [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].
X. Dong, Holographic Entanglement Entropy for General Higher Derivative Gravity, JHEP 01 (2014) 044 [arXiv:1310.5713] [INSPIRE].
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Nishioka, T., Yarom, A. Anomalies and entanglement entropy. J. High Energ. Phys. 2016, 77 (2016). https://doi.org/10.1007/JHEP03(2016)077
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DOI: https://doi.org/10.1007/JHEP03(2016)077