Complexity and action for warped AdS black holes

Journal of High Energy Physics, Sep 2018

Abstract The Complexity=Action conjecture is studied for black holes in Warped AdS3 space, realized as solutions of Einstein gravity plus matter. The time dependence of the action of the Wheeler-DeWitt patch is investigated, both for the non-rotating and the rotating case. The asymptotic growth rate is found to be equal to the Hawking temperature times the Bekenstein-Hawking entropy; this is in agreement with a previous calculation done using the Complexity=Volume conjecture.

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Complexity and action for warped AdS black holes

Journal of High Energy Physics September 2018, 2018:13 | Cite as Complexity and action for warped AdS black holes AuthorsAuthors and affiliations Roberto AuzziStefano BaigueraMatteo GrassiGiuseppe NardelliNicolò Zenoni Open Access Regular Article - Theoretical Physics First Online: 04 September 2018 Received: 26 June 2018 Accepted: 29 August 2018 26 Downloads Abstract The Complexity=Action conjecture is studied for black holes in Warped AdS3 space, realized as solutions of Einstein gravity plus matter. The time dependence of the action of the Wheeler-DeWitt patch is investigated, both for the non-rotating and the rotating case. The asymptotic growth rate is found to be equal to the Hawking temperature times the Bekenstein-Hawking entropy; this is in agreement with a previous calculation done using the Complexity=Volume conjecture. Keywords AdS-CFT Correspondence Black Holes  ArXiv ePrint: 1806.06216 Download to read the full article text Notes 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. References [1] S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [2] H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [3] A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [4] J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE]. [5] J.M. Bardeen, B. Carter and S.W. Hawking, The four laws of black hole mechanics, Commun. Math. Phys. 31 (1973) 161 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [6] J.M. Maldacena, Eternal black holes in Anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [7] T. Hartman and J. Maldacena, Time evolution of entanglement entropy from black hole interiors, JHEP 05 (2013) 014 [arXiv:1303.1080] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [8] L. Susskind, Computational complexity and black hole horizons, Fortsch. Phys. 64 (2016) 24 [Addendum ibid. 64 (2016) 44] [arXiv:1403.5695] [INSPIRE]. [9] L. Susskind, Entanglement is not enough, Fortsch. Phys. 64 (2016) 49 [arXiv:1411.0690] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [10] R. Jefferson and R.C. Myers, Circuit complexity in quantum field theory, JHEP 10 (2017) 107 [arXiv:1707.08570] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [11] 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].ADSMathSciNetCrossRefGoogle Scholar [12] K. Hashimoto, N. Iizuka and S. Sugishita, Time evolution of complexity in Abelian gauge theories, Phys. Rev. D 96 (2017) 126001 [arXiv:1707.03840] [INSPIRE]. [13] R.-Q. Yang, C. Niu, C.-Y. Zhang and K.-Y. Kim, Comparison of holographic and field theoretic complexities for time dependent thermofield double states, JHEP 02 (2018) 082 [arXiv:1710.00600] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [14] R. Khan, C. Krishnan and S. Sharma, Circuit complexity in fermionic field theory, arXiv:1801.07620 [INSPIRE]. [15] L. Hackl and R.C. Myers, Circuit complexity for free fermions, JHEP 07 (2018) 139 [arXiv:1803.10638] [INSPIRE].ADSCrossRefGoogle Scholar [16] P. Caputa et al., Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT, JHEP 11 (2017) 097 [arXiv:1706.07056] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [17] A. Bhattacharyya et al., Path-integral complexity for perturbed CFTs, JHEP 07 (2018) 086 [arXiv:1804.01999] [INSPIRE].ADSCrossRefGoogle Scholar [18] B. Swingle, Entanglement renormalization and holography, Phys. Rev. D 86 (2012) 065007 [arXiv:0905.1317] [INSPIRE]. [19] R.-Q. Yang et al., Axiomatic complexity in quantum field theory and its applications, arXiv:1803.01797 [INSPIRE]. [20] K. Hashimoto, N. Iizuka and S. Sugishita, Thoughts on holographic complexity and its basis-dependence, Phys. Rev. D 98 (2018) 046002 [arXiv:1805.04226] [INSPIRE]. [21] D. Stanford and L. Susskind, Complexity and shock wave geometries, Phys. Rev. D 90 (2014) 126007 [arXiv:1406.2678] [INSPIRE]. [22] A.R. Brown et al., Holographic complexity equals bulk action?, Phys. Rev. Lett. 116 (2016) 191301 [arXiv:1509.07876] [INSPIRE].ADSCrossRefGoogle Scholar [23] A.R. Brown et al., Complexity, action and black holes, Phys. Rev. D 93 (2016) 086006 [arXiv:1512.04993] [INSPIRE]. [24] G. Hayward, Gravitational action for spac (...truncated)


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Roberto Auzzi, Stefano Baiguera, Matteo Grassi, Giuseppe Nardelli, Nicolò Zenoni. Complexity and action for warped AdS black holes, Journal of High Energy Physics, 2018, pp. 13, Volume 2018, Issue 9, DOI: 10.1007/JHEP09(2018)013