Abstract
The back reaction imparted by a uniform distribution of heavy static fundamental quarks on large Nc strongly coupled gauge theory can be holographically realized as a deformation in AdS blackhole background. The presence of back reaction brings significant changes in to the entanglement structure of the strongly coupled boundary theory at finite temperature. Since the deformed blackhole geometry still remains asymptotically AdS, the gauge/ gravity duality allows us to explore the entanglement structure of back reacted plasma in a quantitative way by computing various measures, e.g holographic en tanglement entropy (HEE) and entanglement wedge cross section (EWCS). We explicitly study the variation of those entanglement measures with respect to the uniform density of heavy static fundamental quarks present in the boundary theory. In particular, we notice enhancement of both HEE and EWCS with respect to quark density. We also study the effect of back reaction on the holographic subregion volume complexity. In this analysis we observe an occurrence of logarithmic divergence proportional to the quark density parameter.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.D. Bekenstein, Black holes and the second law, Lett. Nuovo Cim. 4 (1972) 737 [INSPIRE].
S.W. Hawking, Black hole explosions, Nature 248 (1974) 30 [INSPIRE].
C.R. Stephens, G. ’t Hooft and B.F. Whiting, Black hole evaporation without information loss, Class. Quant. Grav. 11 (1994) 621 [gr-qc/9310006] [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.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [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].
J. Erdmenger, Introduction to Gauge/Gravity Duality, PoS(TASI2017)001 (2018) [arXiv:1807.09872] [INSPIRE].
I. Chuang and M. Nielsen, Quantum computation and Quantum in-formation, Cambridge University Press, Cambridge U.K. (2010).
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. Cardy, Entanglement entropy and conformal field theory, J. Phys. A 42 (2009) 504005 [arXiv:0905.4013] [INSPIRE].
P. Calabrese, J. Cardy and E. Tonni, Entanglement entropy of two disjoint intervals in conformal field theory II, J. Stat. Mech. 1101 (2011) P01021 [arXiv:1011.5482] [INSPIRE].
P. Calabrese, J. Cardy and E. Tonni, Entanglement entropy of two disjoint intervals in conformal field theory, J. Stat. Mech. 0911 (2009) P11001 [arXiv:0905.2069] [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].
X. Dong, Holographic Entanglement Entropy for General Higher Derivative Gravity, JHEP 01 (2014) 044 [arXiv:1310.5713] [INSPIRE].
W. Fischler and S. Kundu, Strongly Coupled Gauge Theories: High and Low Temperature Behavior of Non-local Observables, JHEP 05 (2013) 098 [arXiv:1212.2643] [INSPIRE].
S. Kundu and J.F. Pedraza, Aspects of Holographic Entanglement at Finite Temperature and Chemical Potential, JHEP 08 (2016) 177 [arXiv:1602.07353] [INSPIRE].
W. Fischler, A. Kundu and S. Kundu, Holographic Mutual Information at Finite Temperature, Phys. Rev. D 87 (2013) 126012 [arXiv:1212.4764] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
T. Hartman, Entanglement Entropy at Large Central Charge, arXiv:1303.6955 [INSPIRE].
T. Takayanagi and K. Umemoto, Entanglement of purification through holographic duality, Nature Phys. 14 (2018) 573 [arXiv:1708.09393] [INSPIRE].
B.M. Terhal, M. Horodecki, D.W. Leung D.P. DiVincenzo, The entanglement of purification, J. Math. Phys. 43 (2002) 4286 [quant-ph/0202044].
P. Nguyen, T. Devakul, M.G. Halbasch, M.P. Zaletel and B. Swingle, Entanglement of purification: from spin chains to holography, JHEP 01 (2018) 098 [arXiv:1709.07424] [INSPIRE].
K. Babaei Velni, M.R. Mohammadi Mozaffar and M.H. Vahidinia, Some Aspects of Entanglement Wedge Cross-Section, JHEP 05 (2019) 200 [arXiv:1903.08490] [INSPIRE].
N. Jokela and A. Ponni, Notes on entanglement wedge cross sections, J HEP 07 (2019) 087 [arXiv:1904.09582] [INSPIRE].
H.-S. Jeong, K.-Y. Kim and M. Nishida, Reflected Entropy and Entanglement Wedge Cross Section with the First Order Correction, JHEP 12 (2019) 170 [arXiv:1909.02806] [INSPIRE].
L. Susskind, Computational Complexity and Black Hole Horizons, Fortsch. Phys. 64 (2016) 24 [Addendum ibid. 64 (2016) 44] [arXiv:1403.5695] [INSPIRE].
M.A. Nielsen, A geometric approach to quantum circuit lower bounds, quant-ph/0502070.
R. Jefferson and R.C. Myers, Circuit complexity in quantum field theory, JHEP 10 (2017) 107 [arXiv:1707.08570] [INSPIRE].
M. Guo, J. Hernandez, R.C. Myers and S.-M. Ruan, Circuit Complexity for Coherent States, JHEP 10 (2018) 011 [arXiv:1807.07677] [INSPIRE].
S. Chapman et al., Complexity and entanglement for thermofield double states, SciPost Phys. 6 (2019) 034 [arXiv:1810.05151] [INSPIRE].
L. Susskind , Entanglement is not enough, Fortsch. Phys. 64 (2016) 49 [arXiv:1411.0690] [INSPIRE].
L. Susskind and Y. Zhao, Switchbacks and the Bridge to Nowhere, arXiv:1408.2823 [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].
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].
K. Jensen and A. O’Bannon, Holography, Entanglement Entropy and Conformal Field Theories with Boundaries or Defects, Phys. Rev. D 88 (2013) 106006 [arXiv:1309.4523] [INSPIRE].
R. Rodgers, Holographic entanglement entropy from probe M-theory branes, JHEP 03 (2019) 092 [arXiv:1811.12375] [INSPIRE].
L.-Y. Hung, R.C. Myers and M. Smolkin, Some Calculable Contributions to Holographic Entanglement Entropy, JHEP 08 (2011) 039 [arXiv:1105.6055] [INSPIRE].
K. Kontoudi and G. Policastro, Flavor corrections to the entanglement entropy, JHEP 01 (2014) 043 [arXiv:1310.4549] [INSPIRE].
D. Carmi, More on Holographic Volumes, Entanglement and Complexity, arXiv:1709.10463 [INSPIRE].
D. Carmi, On the Shape Dependence of Entanglement Entropy, JHEP 12 (2015) 043 [arXiv:1506.07528] [INSPIRE].
P. Fonda, D. Seminara and E. Tonni, On shape dependence of holographic entanglement entropy in AdS4/CFT3 , JHEP 12 (2015) 037 [arXiv:1510.03664] [INSPIRE].
S. Chakrabortty, Dissipative force on an external quark in heavy quark cloud, Phys. Lett. B 705 (2011) 244 [arXiv:1108.0165] [INSPIRE].
S. Chakrabortty and T.K. Dey, Back reaction effects on the dynamics of heavy probes in heavy quark cloud, JHEP 05 (2016) 094 [arXiv:1602.04761] [INSPIRE].
P.B. Arnold, Quark-Gluon Plasmas and Thermalization, Int. J. Mod. Phys. E 16 (2007) 2555 [arXiv:0708.0812] [INSPIRE].
E. Shuryak, Physics of Strongly coupled Quark-Gluon Plasma, Frog. Part. Nucl. Phys. 62 (2009) 48 [arXiv:0807.3033] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, The Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
P. Liu, Y. Ling, C. Niu and J.-P. Wu, Entanglement of Purification in Holographic Systems, JHEP 09 (2019) 071 [arXiv:1902.02243] [INSPIRE].
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
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2004.06991
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Chakrabortty, S., Pant, S. & Sil, K. Effect of back reaction on entanglement and subregion volume complexity in strongly coupled plasma. J. High Energ. Phys. 2020, 61 (2020). https://doi.org/10.1007/JHEP06(2020)061
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2020)061