Abstract
An analytic static monopole solution is found in global AdS4, in the limit of small backreaction. This solution is mapped in Poincaré patch to a falling monopole configuration, which is dual to a local quench triggered by the injection of a condensate. Choosing boundary conditions which are dual to a time-independent Hamiltonian, we find the same functional form of the energy-momentum tensor as the one of a quench dual to a falling black hole. On the contrary, the details of the spread of entanglement entropy are very different from the falling black hole case, where the quench induces always a higher entropy compared to the vacuum, i.e. ∆S > 0. In the propagation of entanglement entropy for the monopole quench, there is instead a competition between a negative contribution to ∆S due to the scalar condensate and a positive one carried by the freely propagating quasiparticles generated by the energy injection.
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References
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.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].
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].
M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy, vol. 931, Springer (2017), [DOI] [arXiv:1609.01287] [INSPIRE].
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 0504 (2005) P04010 [cond-mat/0503393] [INSPIRE].
J. Abajo-Arrastia, J. Aparicio and E. Lopez, Holographic Evolution of Entanglement Entropy, JHEP 11 (2010) 149 [arXiv:1006.4090] [INSPIRE].
T. Albash and C.V. Johnson, Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches, New J. Phys. 13 (2011) 045017 [arXiv:1008.3027] [INSPIRE].
V. Balasubramanian et al., Thermalization of Strongly Coupled Field Theories, Phys. Rev. Lett. 106 (2011) 191601 [arXiv:1012.4753] [INSPIRE].
V. Balasubramanian et al., Holographic Thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].
A. Buchel, L. Lehner and R.C. Myers, Thermal quenches in N = 2* plasmas, JHEP 08 (2012) 049 [arXiv:1206.6785] [INSPIRE].
A. Buchel, L. Lehner, R.C. Myers and A. van Niekerk, Quantum quenches of holographic plasmas, JHEP 05 (2013) 067 [arXiv:1302.2924] [INSPIRE].
R. Auzzi, S. Elitzur, S.B. Gudnason and E. Rabinovici, On periodically driven AdS/CFT, JHEP 11 (2013) 016 [arXiv:1308.2132] [INSPIRE].
A. Buchel, R.C. Myers and A. van Niekerk, Nonlocal probes of thermalization in holographic quenches with spectral methods, JHEP 02 (2015) 017 [Erratum ibid. 07 (2015) 137] [arXiv:1410.6201] [INSPIRE].
H. Liu and S.J. Suh, Entanglement Tsunami: Universal Scaling in Holographic Thermalization, Phys. Rev. Lett. 112 (2014) 011601 [arXiv:1305.7244] [INSPIRE].
H. Liu and S.J. Suh, Entanglement growth during thermalization in holographic systems, Phys. Rev. D 89 (2014) 066012 [arXiv:1311.1200] [INSPIRE].
H. Casini, H. Liu and M. Mezei, Spread of entanglement and causality, JHEP 07 (2016) 077 [arXiv:1509.05044] [INSPIRE].
T. Langen, R. Geiger, M. Kuhnert, B. Rauer and J. Schmiedmayer, Local emergence of thermal correlations in an isolated quantum many-body system, Nature Phys. 9 (2013).
F. Meinert, M.J. Mark, E. Kirilov, K. Lauber, P. Weinmann, A.J. Daley and H. Nagerl, Quantum Quench in an Atomic One-Dimensional Ising Chain, Phys. Rev. Lett. 111 (2013).
I. Klich and L. Levitov, Quantum Noise as an Entanglement Meter, Phys. Rev. Lett. 102 (2009) 100502 [arXiv:0804.1377] [INSPIRE].
J. Cardy, Measuring Entanglement Using Quantum Quenches, Phys. Rev. Lett. 106 (2011) 150404 [arXiv:1012.5116] [INSPIRE].
P. Calabrese and J. Cardy, Entanglement and correlation functions following a local quench: a conformal field theory approach, J. Stat. Mech. 0710 (2007) P10004 [arXiv:0708.3750] [INSPIRE].
P. Calabrese and J. Cardy, Quantum quenches in 1 + 1 dimensional conformal field theories, J. Stat. Mech. 1606 (2016) 064003 [arXiv:1603.02889] [INSPIRE].
M. Nozaki, T. Numasawa and T. Takayanagi, Quantum Entanglement of Local Operators in Conformal Field Theories, Phys. Rev. Lett. 112 (2014) 111602 [arXiv:1401.0539] [INSPIRE].
P. Caputa, M. Nozaki and T. Takayanagi, Entanglement of local operators in large-N conformal field theories, PTEP 2014 (2014) 093B06 [arXiv:1405.5946] [INSPIRE].
M. Nozaki, Notes on Quantum Entanglement of Local Operators, JHEP 10 (2014) 147 [arXiv:1405.5875] [INSPIRE].
C.T. Asplund, A. Bernamonti, F. Galli and T. Hartman, Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches, JHEP 02 (2015) 171 [arXiv:1410.1392] [INSPIRE].
M. Nozaki, T. Numasawa and T. Takayanagi, Holographic Local Quenches and Entanglement Density, JHEP 05 (2013) 080 [arXiv:1302.5703] [INSPIRE].
C.T. Asplund and A. Bernamonti, Mutual information after a local quench in conformal field theory, Phys. Rev. D 89 (2014) 066015 [arXiv:1311.4173] [INSPIRE].
P. Caputa, J. Simón, A. Štikonas and T. Takayanagi, Quantum Entanglement of Localized Excited States at Finite Temperature, JHEP 01 (2015) 102 [arXiv:1410.2287] [INSPIRE].
M. Rangamani, M. Rozali and A. Vincart-Emard, Dynamics of Holographic Entanglement Entropy Following a Local Quench, JHEP 04 (2016) 069 [arXiv:1512.03478] [INSPIRE].
J.R. David, S. Khetrapal and S.P. Kumar, Universal corrections to entanglement entropy of local quantum quenches, JHEP 08 (2016) 127 [arXiv:1605.05987] [INSPIRE].
C.A. Agón, S.F. Lokhande and J.F. Pedraza, Local quenches, bulk entanglement entropy and a unitary Page curve, JHEP 08 (2020) 152 [arXiv:2004.15010] [INSPIRE].
T. Shimaji, T. Takayanagi and Z. Wei, Holographic Quantum Circuits from Splitting/Joining Local Quenches, JHEP 03 (2019) 165 [arXiv:1812.01176] [INSPIRE].
A. Jahn and T. Takayanagi, Holographic entanglement entropy of local quenches in AdS4/CFT3: a finite-element approach, J. Phys. A 51 (2018) 015401 [arXiv:1705.04705] [INSPIRE].
D.S. Ageev, Sharp disentanglement in holographic charged local quench, arXiv:2003.02918 [INSPIRE].
G. ‘t Hooft, Magnetic Monopoles in Unified Gauge Theories, Nucl. Phys. B 79 (1974) 276 [INSPIRE].
A.R. Lugo and F.A. Schaposnik, Monopole and dyon solutions in AdS space, Phys. Lett. B 467 (1999) 43 [hep-th/9909226] [INSPIRE].
A.R. Lugo, E.F. Moreno and F.A. Schaposnik, Monopole solutions in AdS space, Phys. Lett. B 473 (2000) 35 [hep-th/9911209] [INSPIRE].
S. Bolognesi and D. Tong, Monopoles and Holography, JHEP 01 (2011) 153 [arXiv:1010.4178] [INSPIRE].
P. Sutcliffe, Monopoles in AdS, JHEP 08 (2011) 032 [arXiv:1104.1888] [INSPIRE].
S. Bolognesi, J.N. Laia, D. Tong and K. Wong, A Gapless Hard Wall: Magnetic Catalysis in Bulk and Boundary, JHEP 07 (2012) 162 [arXiv:1204.6029] [INSPIRE].
S. Prem Kumar, A. O’Bannon, A. Pribytok and R. Rodgers, Holographic Coulomb branch solitons, quasinormal modes, and black holes, JHEP 05 (2021) 109 [arXiv:2011.13859] [INSPIRE].
A.R. Lugo, E.F. Moreno and F.A. Schaposnik, Holographic Phase Transition from Dyons in an AdS Black Hole Background, JHEP 03 (2010) 013 [arXiv:1001.3378] [INSPIRE].
A.R. Lugo, E.F. Moreno and F.A. Schaposnik, Holography and AdS4 self-gravitating dyons, JHEP 11 (2010) 081 [arXiv:1007.1482] [INSPIRE].
G.L. Giordano and A.R. Lugo, Holographic phase transitions from higgsed, non abelian charged black holes, JHEP 07 (2015) 172 [arXiv:1501.04033] [INSPIRE].
S. Miyashita and K.-i. Maeda, AdS Monopole Black Hole and Phase Transition, Phys. Rev. D 94 (2016) 124037 [arXiv:1610.07350] [INSPIRE].
A. Esposito, S. Garcia-Saenz, A. Nicolis and R. Penco, Conformal solids and holography, JHEP 12 (2017) 113 [arXiv:1708.09391] [INSPIRE].
G.T. Horowitz and N. Itzhaki, Black holes, shock waves, and causality in the AdS/CFT correspondence, JHEP 02 (1999) 010 [hep-th/9901012] [INSPIRE].
T. Albash and C.V. Johnson, Holographic Studies of Entanglement Entropy in Superconductors, JHEP 05 (2012) 079 [arXiv:1202.2605] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions, and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
M. Berkooz, A. Sever and A. Shomer, ‘Double trace’ deformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].
I. Papadimitriou, Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT, JHEP 05 (2007) 075 [hep-th/0703152] [INSPIRE].
T. Faulkner, G.T. Horowitz and M.M. Roberts, Holographic quantum criticality from multi-trace deformations, JHEP 04 (2011) 051 [arXiv:1008.1581] [INSPIRE].
M.M. Caldarelli, A. Christodoulou, I. Papadimitriou and K. Skenderis, Phases of planar AdS black holes with axionic charge, JHEP 04 (2017) 001 [arXiv:1612.07214] [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [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.D. Blanco, H. Casini, L.-Y. Hung and R.C. Myers, Relative Entropy and Holography, JHEP 08 (2013) 060 [arXiv:1305.3182] [INSPIRE].
A. O’Bannon, J. Probst, R. Rodgers and C.F. Uhlemann, First law of entanglement rates from holography, Phys. Rev. D 96 (2017) 066028 [arXiv:1612.07769] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
T. Albash and C.V. Johnson, Vortex and Droplet Engineering in Holographic Superconductors, Phys. Rev. D 80 (2009) 126009 [arXiv:0906.1795] [INSPIRE].
M. Montull, A. Pomarol and P.J. Silva, The Holographic Superconductor Vortex, Phys. Rev. Lett. 103 (2009) 091601 [arXiv:0906.2396] [INSPIRE].
V. Keranen, E. Keski-Vakkuri, S. Nowling and K.P. Yogendran, Inhomogeneous Structures in Holographic Superfluids: II. Vortices, Phys. Rev. D 81 (2010) 126012 [arXiv:0912.4280] [INSPIRE].
O. Domenech, M. Montull, A. Pomarol, A. Salvio and P.J. Silva, Emergent Gauge Fields in Holographic Superconductors, JHEP 08 (2010) 033 [arXiv:1005.1776] [INSPIRE].
N. Iqbal and H. Liu, Luttinger’s Theorem, Superfluid Vortices, and Holography, Class. Quant. Grav. 29 (2012) 194004 [arXiv:1112.3671] [INSPIRE].
O.J.C. Dias, G.T. Horowitz, N. Iqbal and J.E. Santos, Vortices in holographic superfluids and superconductors as conformal defects, JHEP 04 (2014) 096 [arXiv:1311.3673] [INSPIRE].
K. Maeda, M. Natsuume and T. Okamura, Vortex lattice for a holographic superconductor, Phys. Rev. D 81 (2010) 026002 [arXiv:0910.4475] [INSPIRE].
G. Tallarita, R. Auzzi and A. Peterson, The holographic non-abelian vortex, JHEP 03 (2019) 114 [arXiv:1901.05814] [INSPIRE].
G. Tallarita and R. Auzzi, The holographic vortex lattice using the circular cell method, JHEP 01 (2020) 056 [arXiv:1909.05932] [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].
M. Moosa, Evolution of Complexity Following a Global Quench, JHEP 03 (2018) 031 [arXiv:1711.02668] [INSPIRE].
S. Chapman, H. Marrochio and R.C. Myers, Holographic complexity in Vaidya spacetimes. Part I, JHEP 06 (2018) 046 [arXiv:1804.07410] [INSPIRE].
S. Chapman, H. Marrochio and R.C. Myers, Holographic complexity in Vaidya spacetimes. Part II, JHEP 06 (2018) 114 [arXiv:1805.07262] [INSPIRE].
B. Chen, W.-M. Li, R.-Q. Yang, C.-Y. Zhang and S.-J. Zhang, Holographic subregion complexity under a thermal quench, JHEP 07 (2018) 034 [arXiv:1803.06680] [INSPIRE].
R. Auzzi, G. Nardelli, F.I. Schaposnik Massolo, G. Tallarita and N. Zenoni, On volume subregion complexity in Vaidya spacetime, JHEP 11 (2019) 098 [arXiv:1908.10832] [INSPIRE].
G. Di Giulio and E. Tonni, Subsystem complexity after a global quantum quench, JHEP 05 (2021) 022 [arXiv:2102.02764] [INSPIRE].
D.S. Ageev, I.Y. Aref’eva, A.A. Bagrov and M.I. Katsnelson, Holographic local quench and effective complexity, JHEP 08 (2018) 071 [arXiv:1803.11162] [INSPIRE].
D. Ageev, Holographic complexity of local quench at finite temperature, Phys. Rev. D 100 (2019) 126005 [arXiv:1902.03632] [INSPIRE].
G. Di Giulio and E. Tonni, Subsystem complexity after a local quantum quench, JHEP 08 (2021) 135 [arXiv:2106.08282] [INSPIRE].
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Zenoni, N., Auzzi, R., Caggioli, S. et al. A falling magnetic monopole as a holographic local quench. J. High Energ. Phys. 2021, 48 (2021). https://doi.org/10.1007/JHEP11(2021)048
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DOI: https://doi.org/10.1007/JHEP11(2021)048