Abstract
Introduction of electric field in the D-brane worldvolume induces a horizon in the open string geometry perceived by the brane fluctuations. We study the holographic entanglement entropy (HEE) and subregion complexity (HSC) in these asymptotically AdS geometries in three, four and five dimensions aiming to capture these quantities in the flavor sector introduced by the D-branes. Both the strip and spherical subregions have been considered. We show that the Bekenstein-Hawking entropy associated with the open string horizon, which earlier failed to reproduce the thermal entropy in the boundary, now precisely matches with the entanglement entropy at high temperatures. We check the validity of embedding function theorem while computing the HEE and attempt to reproduce the first law of entanglement thermodynamics, at least at leading order. On the basis of obtained results, we also reflect upon consequences of applying Ryu-Takayanagi proposal on these non-Einstein geometries.
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References
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [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].
E. Witten, A Mini-Introduction To Information Theory, Riv. Nuovo Cim. 43 (2020) 187 [arXiv:1805.11965] [INSPIRE].
L. Bombelli, R.K. Koul, J. Lee and R.D. Sorkin, A Quantum Source of Entropy for Black Holes, Phys. Rev. D 34 (1986) 373 [INSPIRE].
M. Srednicki, Entropy and area, Phys. Rev. Lett. 71 (1993) 666 [hep-th/9303048] [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].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory: A Non-technical introduction, Int. J. Quant. Inf. 4 (2006) 429 [quant-ph/0505193].
P. Calabrese and J. Cardy, Entanglement entropy and conformal field theory, J. Phys. A 42 (2009) 504005 [arXiv:0905.4013] [INSPIRE].
T. Nishioka, S. Ryu and T. Takayanagi, Holographic Entanglement Entropy: An Overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932] [INSPIRE].
T. Takayanagi, Entanglement Entropy from a Holographic Viewpoint, Class. Quant. Grav. 29 (2012) 153001 [arXiv:1204.2450] [INSPIRE].
E. Witten, APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum field theory, Rev. Mod. Phys. 90 (2018) 045003 [arXiv:1803.04993] [INSPIRE].
A.S. Holevo, Quantum information: An introduction by m. hayashi, Quant. Inf. Proc. 6 (2007) 137.
D. Petz and C. Ghinea, Introduction to Quantum Fisher Information, in Quantum Probability and Related Topics, R. Rebolledo and M. Orszag eds., pp. 261–281 (2011) [DOI] [arXiv:1008.2417].
N. Lashkari and M. Van Raamsdonk, Canonical Energy is Quantum Fisher Information, JHEP 04 (2016) 153 [arXiv:1508.00897] [INSPIRE].
M. Miyaji, T. Numasawa, N. Shiba, T. Takayanagi and K. Watanabe, Distance between Quantum States and Gauge-Gravity Duality, Phys. Rev. Lett. 115 (2015) 261602 [arXiv:1507.07555] [INSPIRE].
M. Alishahiha and A. Faraji Astaneh, Holographic Fidelity Susceptibility, Phys. Rev. D 96 (2017) 086004 [arXiv:1705.01834] [INSPIRE].
S. Banerjee, J. Erdmenger and D. Sarkar, Connecting Fisher information to bulk entanglement in holography, JHEP 08 (2018) 001 [arXiv:1701.02319] [INSPIRE].
S.L. Braunstein and C.M. Caves, Statistical distance and the geometry of quantum states, Phys. Rev. Lett. 72 (1994) 3439 [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
N. Engelhardt and A.C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [INSPIRE].
J. Bhattacharya, M. Nozaki, T. Takayanagi and T. Ugajin, Thermodynamical Property of Entanglement Entropy for Excited States, Phys. Rev. Lett. 110 (2013) 091602 [arXiv:1212.1164] [INSPIRE].
D. Allahbakhshi, M. Alishahiha and A. Naseh, Entanglement Thermodynamics, JHEP 08 (2013) 102 [arXiv:1305.2728] [INSPIRE].
R. Mishra and H. Singh, Perturbative entanglement thermodynamics for AdS spacetime: Renormalization, JHEP 10 (2015) 129 [arXiv:1507.03836] [INSPIRE].
A. Bhattacharya and S. Roy, Holographic entanglement entropy and entanglement thermodynamics of ‘black’ non-SUSY D3 brane, Phys. Lett. B 781 (2018) 232 [arXiv:1712.03740] [INSPIRE].
D.-W. Pang, Entanglement thermodynamics for nonconformal D-branes, Phys. Rev. D 88 (2013) 126001 [arXiv:1310.3676] [INSPIRE].
S. Chakraborty, P. Dey, S. Karar and S. Roy, Entanglement thermodynamics for an excited state of Lifshitz system, JHEP 04 (2015) 133 [arXiv:1412.1276] [INSPIRE].
A. Bhattacharya, K.T. Grosvenor and S. Roy, Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime, Phys. Rev. D 100 (2019) 126004 [arXiv:1905.02220] [INSPIRE].
N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].
A. Kundu and S. Kundu, Steady-state Physics, Effective Temperature Dynamics in Holography, Phys. Rev. D 91 (2015) 046004 [arXiv:1307.6607] [INSPIRE].
A. Kundu, Effective Temperature in Steady-state Dynamics from Holography, JHEP 09 (2015) 042 [arXiv:1507.00818] [INSPIRE].
A. Banerjee, A. Kundu and S. Kundu, Flavour Fields in Steady State: Stress Tensor and Free Energy, JHEP 02 (2016) 102 [arXiv:1512.05472] [INSPIRE].
T. Azeyanagi, A. Karch, T. Takayanagi and E.G. Thompson, Holographic calculation of boundary entropy, JHEP 03 (2008) 054 [arXiv:0712.1850] [INSPIRE].
H.-C. Chang and A. Karch, Entanglement Entropy for Probe Branes, JHEP 01 (2014) 180 [arXiv:1307.5325] [INSPIRE].
K. Kontoudi and G. Policastro, Flavor corrections to the entanglement entropy, JHEP 01 (2014) 043 [arXiv:1310.4549] [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
L. Susskind, Computational Complexity and Black Hole Horizons, Fortsch. Phys. 64 (2016) 24 [Addendum ibid. 64 (2016) 44] [arXiv:1403.5695] [INSPIRE].
D. Stanford and L. Susskind, Complexity and Shock Wave Geometries, Phys. Rev. D 90 (2014) 126007 [arXiv:1406.2678] [INSPIRE].
A.R. Brown, D.A. Roberts, L. Susskind, B. Swingle and Y. Zhao, Holographic Complexity Equals Bulk Action?, Phys. Rev. Lett. 116 (2016) 191301 [arXiv:1509.07876] [INSPIRE].
A.R. Brown, D.A. Roberts, L. Susskind, B. Swingle and Y. Zhao, Complexity, action, and black holes, Phys. Rev. D 93 (2016) 086006 [arXiv:1512.04993] [INSPIRE].
S. Chapman, M.P. Heller, H. Marrochio and F. Pastawski, Toward a Definition of Complexity for Quantum Field Theory States, Phys. Rev. Lett. 120 (2018) 121602 [arXiv:1707.08582] [INSPIRE].
R. Jefferson and R.C. Myers, Circuit complexity in quantum field theory, JHEP 10 (2017) 107 [arXiv:1707.08570] [INSPIRE].
R. Khan, C. Krishnan and S. Sharma, Circuit Complexity in Fermionic Field Theory, Phys. Rev. D 98 (2018) 126001 [arXiv:1801.07620] [INSPIRE].
L. Hackl and R.C. Myers, Circuit complexity for free fermions, JHEP 07 (2018) 139 [arXiv:1803.10638] [INSPIRE].
M.A. Nielsen, M.R. Dowling, M. Gu and A.C. Doherty, Quantum Computation as Geometry, Science 311 (2006) 1133 [quant-ph/0603161].
M.R. Dowling and M.A. Nielsen, The geometry of quantum computation, quant-ph/0701004.
P. Caputa, N. Kundu, M. Miyaji, T. Takayanagi and K. Watanabe, Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories, Phys. Rev. Lett. 119 (2017) 071602 [arXiv:1703.00456] [INSPIRE].
P. Caputa, N. Kundu, M. Miyaji, T. Takayanagi and K. Watanabe, Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT, JHEP 11 (2017) 097 [arXiv:1706.07056] [INSPIRE].
R. Abt et al., Topological Complexity in AdS3/CFT2, Fortsch. Phys. 66 (2018) 1800034 [arXiv:1710.01327] [INSPIRE].
P. Caputa and J.M. Magan, Quantum Computation as Gravity, Phys. Rev. Lett. 122 (2019) 231302 [arXiv:1807.04422] [INSPIRE].
M. Flory and M.P. Heller, Geometry of Complexity in Conformal Field Theory, Phys. Rev. Res. 2 (2020) 043438 [arXiv:2005.02415] [INSPIRE].
J. Erdmenger, M. Gerbershagen and A.-L. Weigel, Complexity measures from geometric actions on Virasoro and Kac-Moody orbits, JHEP 11 (2020) 003 [arXiv:2004.03619] [INSPIRE].
P. Caputa and I. MacCormack, Geometry and Complexity of Path Integrals in Inhomogeneous CFTs, arXiv:2004.04698.
M. Alishahiha, Holographic Complexity, Phys. Rev. D 92 (2015) 126009 [arXiv:1509.06614] [INSPIRE].
O. Ben-Ami and D. Carmi, On Volumes of Subregions in Holography and Complexity, JHEP 11 (2016) 129 [arXiv:1609.02514] [INSPIRE].
D. Carmi, R.C. Myers and P. Rath, Comments on Holographic Complexity, JHEP 03 (2017) 118 [arXiv:1612.00433] [INSPIRE].
P. Roy and T. Sarkar, Note on subregion holographic complexity, Phys. Rev. D 96 (2017) 026022 [arXiv:1701.05489] [INSPIRE].
A. Bhattacharya and S. Roy, Holographic entanglement entropy, subregion complexity and Fisher information metric of ‘black’ non-SUSY D3 brane, Phys. Lett. B 800 (2020) 135032 [arXiv:1807.06361] [INSPIRE].
C.A. Agón, M. Headrick and B. Swingle, Subsystem Complexity and Holography, JHEP 02 (2019) 145 [arXiv:1804.01561] [INSPIRE].
M. Alishahiha, K. Babaei Velni and M.R. Mohammadi Mozaffar, Black hole subregion action and complexity, Phys. Rev. D 99 (2019) 126016 [arXiv:1809.06031] [INSPIRE].
T. Takayanagi, Holographic Spacetimes as Quantum Circuits of Path-Integrations, JHEP 12 (2018) 048 [arXiv:1808.09072] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
O. DeWolfe, D.Z. Freedman and H. Ooguri, Holography and defect conformal field theories, Phys. Rev. D 66 (2002) 025009 [hep-th/0111135] [INSPIRE].
C. Núñez, A. Paredes and A.V. Ramallo, Unquenched Flavor in the Gauge/Gravity Correspondence, Adv. High Energy Phys. 2010 (2010) 196714 [arXiv:1002.1088] [INSPIRE].
A.A. Tseytlin, On nonAbelian generalization of Born-Infeld action in string theory, Nucl. Phys. B 501 (1997) 41 [hep-th/9701125] [INSPIRE].
A. Banerjee, A. Kundu and R. Poojary, Maximal Chaos from Strings, Branes and Schwarzian Action, JHEP 06 (2019) 076 [arXiv:1811.04977] [INSPIRE].
A. Banerjee, A. Kundu and S. Kundu, Emergent Horizons and Causal Structures in Holography, JHEP 09 (2016) 166 [arXiv:1605.07368] [INSPIRE].
A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].
T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, Quarks in an external electric field in finite temperature large N gauge theory, JHEP 08 (2008) 092 [arXiv:0709.1554] [INSPIRE].
J. Erdmenger, R. Meyer and J.P. Shock, AdS/CFT with flavour in electric and magnetic Kalb-Ramond fields, JHEP 12 (2007) 091 [arXiv:0709.1551] [INSPIRE].
K. Narayan, T. Takayanagi and S.P. Trivedi, AdS plane waves and entanglement entropy, JHEP 04 (2013) 051 [arXiv:1212.4328] [INSPIRE].
K. Narayan, Non-conformal brane plane waves and entanglement entropy, Phys. Lett. B 726 (2013) 370 [arXiv:1304.6697] [INSPIRE].
D. Mukherjee and K. Narayan, AdS plane waves, entanglement and mutual information, Phys. Rev. D 90 (2014) 026003 [arXiv:1405.3553] [INSPIRE].
R. Mishra and H. Singh, Entanglement asymmetry for boosted black branes and the bound, Int. J. Mod. Phys. A 32 (2017) 1750091 [arXiv:1603.06058] [INSPIRE].
B. Swingle and T. Senthil, Universal crossovers between entanglement entropy and thermal entropy, Phys. Rev. B 87 (2013) 045123 [arXiv:1112.1069] [INSPIRE].
X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP 06 (2012) 041 [arXiv:1201.1905] [INSPIRE].
A. Karch, A. O’Bannon and E. Thompson, The Stress-Energy Tensor of Flavor Fields from AdS/CFT, JHEP 04 (2009) 021 [arXiv:0812.3629] [INSPIRE].
C. Ecker, D. Grumiller and S.A. Stricker, Evolution of holographic entanglement entropy in an anisotropic system, JHEP 07 (2015) 146 [arXiv:1506.02658] [INSPIRE].
C. Ecker, Entanglement Entropy from Numerical Holography, Ph.D. Thesis, Technische Universität Wien (2018) [arXiv:1809.05529] [INSPIRE].
N. Seiberg, L. Susskind and N. Toumbas, Strings in background electric field, space/time noncommutativity and a new noncritical string theory, JHEP 06 (2000) 021 [hep-th/0005040] [INSPIRE].
M. Berkooz, Nonlocal field theories and the noncommutative torus, Phys. Lett. B 430 (1998) 237 [hep-th/9802069] [INSPIRE].
W.-H. Huang, Generalized Gravitational Entropy of Interacting Scalar Field and Maxwell Field, Phys. Lett. B 739 (2014) 365 [arXiv:1409.4893] [INSPIRE].
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Banerjee, A., Bhattacharya, A. & Maulik, S. HEE and HSC for flavors: perturbative structure in open string geometries. J. High Energ. Phys. 2021, 212 (2021). https://doi.org/10.1007/JHEP07(2021)212
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DOI: https://doi.org/10.1007/JHEP07(2021)212