Abstract
We compute the ultraviolet divergences of holographic subregion complexity for the left and right factors of the thermofield double state in warped AdS3 black holes, both for the action and the volume conjectures. Besides the linear divergences, which are also present in the BTZ black hole, additional logarithmic divergences appear. For the action conjecture, these log divergences are not affected by the arbitrarity in the length scale associated with the counterterm needed to ensure reparameterization invariance. We find that the subregion action complexity obeys the superadditivity property for the thermofield double in warped AdS3, independently from the action counterterm coefficient. We study the temperature dependence of subregion complexity at constant angular momentum and we find that it is correlated with the sign of the specific heat.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, Eternal black holes in Anti-de Sitter, JHEP04 (2003) 021 [hep-th/0106112] [INSPIRE].
T. Hartman and J. Maldacena, Time evolution of entanglement entropy from black hole interiors, JHEP05 (2013) 014 [arXiv:1303.1080] [INSPIRE].
L. Susskind, Computational complexity and black hole horizons, Fortsch. Phys. 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].
L. Susskind, Entanglement is not enough, Fortsch. Phys. 64 (2016) 49 [arXiv:1411.0690] [INSPIRE].
M.A. Nielsen, A geometric approach to quantum circuit lower bounds, Quant. Inf. Comput. 6 (2006) 213 [quant-ph/0502070].
M.R. Dowling and M.A. Nielsen, The geometry of quantum computation, Quant. Inf. Comput. 8 (2008) 861 [quant-ph/0701004].
R. Jefferson and R.C. Myers, Circuit complexity in quantum field theory, JHEP10 (2017) 107 [arXiv:1707.08570] [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].
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].
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, JHEP02 (2018) 082 [arXiv:1710.00600] [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, JHEP07 (2018) 139 [arXiv:1803.10638] [INSPIRE].
S. Chapman et al., Complexity and entanglement for thermofield double states, SciPost Phys. 6 (2019) 034 [arXiv:1810.05151] [INSPIRE].
P. Caputa et al., Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT, JHEP11 (2017) 097 [arXiv:1706.07056] [INSPIRE].
A. Bhattacharyya et al., Path-integral complexity for perturbed CFTs, JHEP07 (2018) 086 [arXiv:1804.01999] [INSPIRE].
A.R. Brown et al., Holographic complexity equals bulk action?, Phys. Rev. Lett. 116 (2016) 191301 [arXiv:1509.07876] [INSPIRE].
A.R. Brown et al., Complexity, action and black holes, Phys. Rev. D 93 (2016) 086006 [arXiv:1512.04993] [INSPIRE].
G. Hayward, Gravitational action for space-times with nonsmooth boundaries, Phys. Rev. D 47 (1993) 3275 [INSPIRE].
L. Lehner, R.C. Myers, E. Poisson and R.D. Sorkin, Gravitational action with null boundaries, Phys. Rev. D 94 (2016) 084046 [arXiv:1609.00207] [INSPIRE].
J. Couch, W. Fischler and P.H. Nguyen, Noether charge, black hole volume and complexity, JHEP03 (2017) 119 [arXiv:1610.02038] [INSPIRE].
D. Carmi et al., On the time dependence of holographic complexity, JHEP11 (2017) 188 [arXiv:1709.10184] [INSPIRE].
R.-Q. Yang et al., Principles and symmetries of complexity in quantum field theory, Eur. Phys. J.C 79 (2019) 109 [arXiv:1803.01797] [INSPIRE].
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].
S. Chapman, H. Marrochio and R.C. Myers, Complexity of formation in holography, JHEP01 (2017) 062 [arXiv:1610.08063] [INSPIRE].
R.-G. Cai et al., Action growth for AdS black holes, JHEP09 (2016) 161 [arXiv:1606.08307] [INSPIRE].
A. Reynolds and S.F. Ross, Divergences in holographic complexity, Class. Quant. Grav. 34 (2017) 105004 [arXiv:1612.05439] [INSPIRE].
M. Moosa, Evolution of complexity following a global quench, JHEP03 (2018) 031 [arXiv:1711.02668] [INSPIRE].
M. Moosa, Divergences in the rate of complexification, Phys. Rev. D 97 (2018) 106016 [arXiv:1712.07137] [INSPIRE].
S. Chapman, H. Marrochio and R.C. Myers, Holographic complexity in Vaidya spacetimes. Part I, JHEP06 (2018) 046 [arXiv:1804.07410] [INSPIRE].
S. Chapman, H. Marrochio and R.C. Myers, Holographic complexity in Vaidya spacetimes. Part II, JHEP06 (2018) 114 [arXiv:1805.07262] [INSPIRE].
J.L.F. Barbon and E. Rabinovici, Holographic complexity and spacetime singularities, JHEP01 (2016) 084 [arXiv:1509.09291] [INSPIRE].
S. Bolognesi, E. Rabinovici and S.R. Roy, On some universal features of the holographic quantum complexity of bulk singularities, JHEP06 (2018) 016 [arXiv:1802.02045] [INSPIRE].
B. Swingle and Y. Wang, Holographic complexity of Einstein-Maxwell-dilaton gravity, JHEP09 (2018) 106 [arXiv:1712.09826] [INSPIRE].
Y.-S. An and R.-H. Peng, Effect of the dilaton on holographic complexity growth, Phys. Rev. D 97 (2018) 066022 [arXiv:1801.03638] [INSPIRE].
M. Headrick, V.E. Hubeny, A. Lawrence and M. Rangamani, Causality & holographic entanglement entropy, JHEP12 (2014) 162 [arXiv:1408.6300] [INSPIRE].
M. Alishahiha, Holographic complexity, Phys. Rev. D 92 (2015) 126009 [arXiv:1509.06614] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
D. Carmi, R.C. Myers and P. Rath, Comments on holographic complexity, JHEP03 (2017) 118 [arXiv:1612.00433] [INSPIRE].
O. Ben-Ami and D. Carmi, On volumes of subregions in holography and complexity, JHEP11 (2016) 129 [arXiv:1609.02514] [INSPIRE].
R. Abt et al., Topological complexity in AdS 3/CFT 2, Fortsch. Phys. 66 (2018) 1800034 [arXiv:1710.01327] [INSPIRE].
R. Abt et al., Holographic subregion complexity from kinematic space, JHEP01 (2019) 012 [arXiv:1805.10298] [INSPIRE].
P. Roy and T. Sarkar, Note on subregion holographic complexity, Phys. Rev. D 96 (2017) 026022 [arXiv:1701.05489] [INSPIRE].
P. Roy and T. Sarkar, Subregion holographic complexity and renormalization group flows, Phys. Rev. D 97 (2018) 086018 [arXiv:1708.05313] [INSPIRE].
A. Bhattacharya, K.T. Grosvenor and S. Roy, Higher-order corrections to holographic entanglement entropy and subregion complexity in the AdS black hole background, arXiv:1905.02220 [INSPIRE].
C.A. Agón, M. Headrick and B. Swingle, Subsystem complexity and holography, JHEP02 (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].
E. Cáceres, J. Couch, S. Eccles and W. Fischler, Holographic purification complexity, Phys. Rev.D 99 (2019) 086016 [arXiv:1811.10650] [INSPIRE].
M. Ghodrati et al., The connection between holographic entanglement and complexity of purification, JHEP09 (2019) 009 [arXiv:1902.02475] [INSPIRE].
D. Anninos et al., Warped AdS 3Black Holes, JHEP03 (2009) 130 [arXiv:0807.3040] [INSPIRE].
D. Anninos, Hopfing and puffing warped Anti-de Sitter space, JHEP09 (2009) 075 [arXiv:0809.2433] [INSPIRE].
S. Detournay, T. Hartman and D.M. Hofman, Warped conformal field theory, Phys. Rev. D 86 (2012) 124018 [arXiv:1210.0539] [INSPIRE].
D.M. Hofman and B. Rollier, Warped conformal field theory as lower spin gravity, Nucl. Phys. B 897 (2015) 1 [arXiv:1411.0672] [INSPIRE].
K. Jensen, Locality and anomalies in warped conformal field theory, JHEP12 (2017) 111 [arXiv:1710.11626] [INSPIRE].
D. Anninos, J. Samani and E. Shaghoulian, Warped entanglement entropy, JHEP02 (2014) 118 [arXiv:1309.2579] [INSPIRE].
A. Castro, D.M. Hofman and N. Iqbal, Entanglement entropy in warped conformal field theories, JHEP02 (2016) 033 [arXiv:1511.00707] [INSPIRE].
T. Azeyanagi, S. Detournay and M. Riegler, Warped black holes in lower-spin gravity, Phys. Rev. D 99 (2019) 026013 [arXiv:1801.07263] [INSPIRE].
W. Song, Q. Wen and J. Xu, Generalized gravitational entropy for warped Anti–de Sitter space, Phys. Rev. Lett.117 (2016) 011602 [arXiv:1601.02634] [INSPIRE].
W. Song, Q. Wen and J. Xu, Modifications to holographic entanglement entropy in warped CFT, JHEP02 (2017) 067 [arXiv:1610.00727] [INSPIRE].
M. Ghodrati, Complexity growth in massive gravity theories, the effects of chirality and more, Phys. Rev. D 96 (2017) 106020 [arXiv:1708.07981] [INSPIRE].
R. Auzzi, S. Baiguera and G. Nardelli, Volume and complexity for warped AdS black holes, JHEP06 (2018) 063 [arXiv:1804.07521] [INSPIRE].
R. Auzzi et al., Complexity and action for warped AdS black holes, JHEP09 (2018) 013 [arXiv:1806.06216] [INSPIRE].
H. Dimov, R.C. Rashkov and T. Vetsov, Thermodynamic information geometry and complexity growth of a warped AdS black hole and the warped AdS 3/CFT 2correspondence, Phys. Rev. D 99 (2019) 126007 [arXiv:1902.02433] [INSPIRE].
K.A. Moussa, G. Clement and C. Leygnac, The black holes of topologically massive gravity, Class. Quant. Grav. 20 (2003) L277 [gr-qc/0303042] [INSPIRE].
A. Bouchareb and G. Clement, Black hole mass and angular momentum in topologically massive gravity, Class. Quant. Grav. 24 (2007) 5581 [arXiv:0706.0263] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2 + 1) black hole, Phys. Rev. D 48 (1993) 1506 [Erratum ibid. D 88 (2013) 069902] [gr-qc/9302012] [INSPIRE].
M. Bañados, G. Barnich, G. Compere and A. Gomberoff, Three dimensional origin of Godel spacetimes and black holes, Phys. Rev. D 73 (2006) 044006 [hep-th/0512105] [INSPIRE].
G. Barnich and G. Compere, Conserved charges and thermodynamics of the spinning Godel black hole, Phys. Rev. Lett. 95 (2005) 031302 [hep-th/0501102] [INSPIRE].
G. Clement, Warped AdS 3black holes in new massive gravity, Class. Quant. Grav. 26 (2009) 105015 [arXiv:0902.4634] [INSPIRE].
F. Jugeau, G. Moutsopoulos and P. Ritter, From accelerating and Poincaré coordinates to black holes in spacelike warped AdS 3and back, Class. Quant. Grav. 28 (2011) 035001 [arXiv:1007.1961] [INSPIRE].
R.-Q. Yang, C. Niu and K.-Y. Kim, Surface counterterms and regularized holographic complexity, JHEP09 (2017) 042 [arXiv:1701.03706] [INSPIRE].
A. Akhavan and F. Omidi, On the Role of Counterterms in Holographic Complexity, arXiv:1906.09561 [INSPIRE].
P.C.W. Davies, Thermodynamics of black holes, Proc. Roy. Soc. Lond. A 353 (1977) 499.
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
ArXiv ePrint: 1906.09345
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Auzzi, R., Baiguera, S., Mitra, A. et al. Subsystem complexity in warped AdS. J. High Energ. Phys. 2019, 114 (2019). https://doi.org/10.1007/JHEP09(2019)114
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2019)114