Holographic heat engines, entanglement entropy, and renormalization group flow. (English) Zbl 1475.83071
Summary: We explore a fruitful connection between the physics of conformal field theories (CFTs) in \(d\)-dimensional Minkowski spacetime and the extended gravitational thermodynamics of hyperbolic black holes in \((d+1)\)-dimensional anti-de Sitter spacetime. The CFTs are reduced on a region bounded by a sphere. We show that renormalization group flows between CFTs are specific thermodynamic processes in the \((p,V)\) plane, where the irreversibility of coarse-graining flows from the ultraviolet to the infrared corresponds to the second law of thermodynamics, preventing heat from flowing from low temperature to high. We observe that holographic heat engines using the black holes as a working substance correspond to specific combinations of CFT flows and deformations. We construct three special engines whose net heat and work can be described in terms of changes of entanglement entropy across the sphere. Engine efficiencies emerge as simple functions of the ratio of the number of degrees of freedom of two CFTs.
MSC:
| 83C57 | Black holes |
| 81T35 | Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) |
| 80A10 | Classical and relativistic thermodynamics |
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 81P42 | Entanglement measures, concurrencies, separability criteria |
References:
| [1] | Ryu, S.; Takayanagi, T., Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett., 96, (2006) · Zbl 1228.83110 · doi:10.1103/PhysRevLett.96.181602 |
| [2] | Ryu, S.; Takayanagi, T., Aspects of holographic entanglement entropy, J. High Energy Phys., JHEP08(2006), 045, (2006) · doi:10.1088/1126-6708/2006/08/045 |
| [3] | Maldacena, J. M., The large n limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys., 2, 231-252, (1998) · Zbl 0914.53047 · doi:10.4310/ATMP.1998.v2.n2.a1 |
| [4] | Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M., Gauge theory correlators from non-critical string theory, Phys. Lett. B, 428, 105-114, (1998) · Zbl 1355.81126 · doi:10.1016/S0370-2693(98)00377-3 |
| [5] | Witten, E., Anti-de sitter space and holography, Adv. Theor. Math. Phys., 2, 253-291, (1998) · Zbl 0914.53048 · doi:10.4310/ATMP.1998.v2.n2.a2 |
| [6] | Witten, E., Anti-de sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys., 2, 505-532, (1998) · Zbl 1057.81550 · doi:10.4310/ATMP.1998.v2.n3.a3 |
| [7] | Myers, R. C.; Sinha, A., Seeing a c-theorem with holography, Phys. Rev. D, 82, (2010) · doi:10.1103/PhysRevD.82.046006 |
| [8] | Myers, R. C.; Sinha, A., Holographic c-theorems in arbitrary dimensions, J. High Energy Phys., JHEP01(2011), 125, (2011) · Zbl 1214.83036 · doi:10.1007/JHEP01(2011)125 |
| [9] | Casini, H.; Huerta, M.; Myers, R. C., Towards a derivation of holographic entanglement entropy, J. High Energy Phys., JHEP05(2011), 036, (2011) · Zbl 1296.81073 · doi:10.1007/JHEP05(2011)036 |
| [10] | Cardy, J. L., Is there a c theorem in four-dimensions?, Phys. Lett. B, 215, 749-752, (1988) · doi:10.1016/0370-2693(88)90054-8 |
| [11] | Casini, H.; Huerta, M., A finite entanglement entropy and the c-theorem, Phys. Lett. B, 600, 142-150, (2004) · Zbl 1247.81021 · doi:10.1016/j.physletb.2004.08.072 |
| [12] | Casini, H.; Huerta, M., On the RG running of the entanglement entropy of a circle, Phys. Rev. D, 85, (2012) · Zbl 1397.81034 · doi:10.1103/PhysRevD.85.125016 |
| [13] | Casini, H.; Test, E.; Torroba, G., Markov property of the conformal field theory vacuum and the a theorem, Phys. Rev. Lett., 118, (2017) · doi:10.1103/PhysRevLett.118.261602 |
| [14] | Bekenstein, J. D., Black holes and entropy, Phys. Rev. D, 7, 2333-2346, (1973) · Zbl 1369.83037 · doi:10.1103/PhysRevD.7.2333 |
| [15] | Bekenstein, J. D., Generalized second law of thermodynamics in black hole physics, Phys. Rev. D, 9, 3292-3300, (1974) · doi:10.1103/PhysRevD.9.3292 |
| [16] | Hawking, S., Particle creation by black holes, Commun. Math. Phys., 43, 199-220, (1975) · Zbl 1378.83040 · doi:10.1007/BF02345020 |
| [17] | Hawking, S., Black holes and thermodynamics, Phys. Rev. D, 13, 191-197, (1976) · doi:10.1103/PhysRevD.13.191 |
| [18] | Henneaux, M.; Teitelboim, C., The cosmological constant as a canonical variable, Phys. Lett. B, 143, 415-420, (1984) · doi:10.1016/0370-2693(84)91493-X |
| [19] | Teitelboim, C., The cosmological constant as a thermodynamic black hole parameter, Phys. Lett. B, 158, 293-297, (1985) · doi:10.1016/0370-2693(85)91186-4 |
| [20] | Henneaux, M.; Teitelboim, C., The cosmological constant and general covariance, Phys. Lett. B, 222, 195-199, (1989) · doi:10.1016/0370-2693(89)91251-3 |
| [21] | Caldarelli, M. M.; Cognola, G.; Klemm, D., Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories, Class. Quantum Grav., 17, 399-420, (2000) · Zbl 0945.83019 · doi:10.1088/0264-9381/17/2/310 |
| [22] | Wang, S.; Wu, S-Q; Xie, F.; Dan, L., The first laws of thermodynamics of the (2 + 1)-dimensional BTZ black holes and Kerr – de Sitter spacetimes, Chin. Phys. Lett., 23, 1096-1098, (2006) · doi:10.1088/0256-307X/23/5/009 |
| [23] | Sekiwa, Y., Thermodynamics of de Sitter black holes: thermal cosmological constant, Phys. Rev. D, 73, (2006) · doi:10.1103/PhysRevD.73.084009 |
| [24] | Larranaga Rubio, E. A., Stringy generalization of the first law of thermodynamics for rotating BTZ black hole with a cosmological constant as state parameter, (2007) |
| [25] | Kastor, D.; Ray, S.; Traschen, J., Enthalpy and the mechanics of AdS black holes, Class. Quantum Grav., 26, (2009) · Zbl 1178.83030 · doi:10.1088/0264-9381/26/19/195011 |
| [26] | Kubiznak, D.; Mann, R. B.; Teo, M., Black hole chemistry: thermodynamics with lambda, Class. Quantum Grav., 34, (2017) · Zbl 1368.83002 · doi:10.1088/1361-6382/aa5c69 |
| [27] | Dolan, B. P., The compressibility of rotating black holes in \(D\)-dimensions, Class. Quantum Grav., 31, (2014) · Zbl 1285.83009 · doi:10.1088/0264-9381/31/3/035022 |
| [28] | Johnson, C. V., Holographic heat engines, Class. Quantum Grav., 31, (2014) · Zbl 1304.83031 · doi:10.1088/0264-9381/31/20/205002 |
| [29] | Kastor, D.; Ray, S.; Traschen, J., Chemical potential in the first law for holographic entanglement entropy, J. High Energy Phys., JHEP11(2014), 120, (2014) · doi:10.1007/JHEP11(2014)120 |
| [30] | Girardello, L.; Petrini, M.; Porrati, M.; Zaffaroni, A., Novel local CFT and exact results on perturbations of \(N=4\) super Yang Mills from AdS dynamics, J. High Energy Phys., JHEP12(1998), 022, (1998) · Zbl 0949.81053 · doi:10.1088/1126-6708/1998/12/022 |
| [31] | Distler, J.; Zamora, F., Nonsupersymmetric conformal field theories from stable anti-de Sitter spaces, Adv. Theor. Math. Phys., 2, 1405-1439, (1999) · Zbl 1059.81597 · doi:10.4310/ATMP.1998.v2.n6.a6 |
| [32] | Johnson, C. V., Gauss-Bonnet black holes and holographic heat engines beyond large \(N\), Class. Quantum Grav., 33, (2016) · Zbl 1351.83048 · doi:10.1088/0264-9381/33/21/215009 |
| [33] | Johnson, C. V., Born-Infeld AdS black holes as heat engines, Class. Quantum Grav., 33, (2016) · Zbl 1346.83042 · doi:10.1088/0264-9381/33/13/135001 |
| [34] | Rosso, F., Holographic heat engines and static black holes: a general efficiency formula, Int. J. Mod. Phys. D, 28, 1950030, (2019) · doi:10.1142/S0218271819500305 |
| [35] | Emparan, R.; Johnson, C. V.; Myers, R. C., Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D, 60, (1999) · doi:10.1103/PhysRevD.60.104001 |
| [36] | Emparan, R., AdS/CFT duals of topological black holes and the entropy of zero energy states, J. High Energy Phys., JHEP06(1999), 036, (1999) · Zbl 0951.83021 · doi:10.1088/1126-6708/1999/06/036 |
| [37] | Cai, R-G; Wang, A., Thermodynamics and stability of hyperbolic charged black holes, Phys. Rev. D, 70, (2004) · doi:10.1103/PhysRevD.70.064013 |
| [38] | Birmingham, D., Topological black holes in anti-de Sitter space, Class. Quantum Grav., 16, 1197-1205, (1999) · Zbl 0933.83025 · doi:10.1088/0264-9381/16/4/009 |
| [39] | Mann, R. B., Pair production of topological anti-de Sitter black holes, Class. Quantum Grav., 14, L109-L114, (1997) · Zbl 0873.53073 |
| [40] | Vanzo, L., Black holes with unusual topology, Phys. Rev. D, 56, 6475-6483, (1997) · doi:10.1103/PhysRevD.56.6475 |
| [41] | Brill, D. R.; Louko, J.; Peldan, P., Thermodynamics of (3 + 1)-dimensional black holes with toroidal or higher genus horizons, Phys. Rev. D, 56, 3600-3610, (1997) · doi:10.1103/PhysRevD.56.3600 |
| [42] | Emparan, R., AdS membranes wrapped on surfaces of arbitrary genus, Phys. Lett. B, 432, 74-82, (1998) · doi:10.1016/S0370-2693(98)00625-X |
| [43] | Smarr, L., Mass formula for Kerr black holes, Phys. Rev. Lett., 30, 71-73, (1973) · doi:10.1103/PhysRevLett.30.71 |
| [44] | Blanco, D. D.; Casini, H.; Hung, L-Y; Myers, R. C., Relative entropy and holography, J. High Energy Phys., JHEP08(2013), 060, (2013) · Zbl 1342.83128 · doi:10.1007/JHEP08(2013)060 |
| [45] | Leigh, R. G.; Strassler, M. J., Exactly marginal operators and duality in four-dimensional \(N=1\) supersymmetric gauge theory, Nucl. Phys. B, 447, 95-136, (1995) · Zbl 1009.81570 · doi:10.1016/0550-3213(95)00261-P |
| [46] | Karch, A.; Lust, D.; Miemiec, A., New \(N=1\) superconformal field theories and their supergravity description, Phys. Lett. B, 454, 265-269, (1999) · Zbl 1058.81712 · doi:10.1016/S0370-2693(99)00392-5 |
| [47] | Khavaev, A.; Pilch, K.; Warner, N. P., New vacua of gauged \(N=8\) supergravity in five-dimensions, Phys. Lett. B, 487, 14-21, (2000) · Zbl 1050.81686 · doi:10.1016/S0370-2693(00)00795-4 |
| [48] | Freedman, D. Z.; Gubser, S. S.; Pilch, K.; Warner, N. P., Renormalization group flows from holography supersymmetry and a c-theorem, Adv. Theor. Math. Phys., 3, 363-417, (1999) · Zbl 0976.83067 · doi:10.4310/ATMP.1999.v3.n2.a7 |
| [49] | Pilch, K.; Warner, N. P., \(N = 1\) supersymmetric renormalization group flows from IIB supergravity, Adv. Theor. Math. Phys., 4, 627-677, (2002) · Zbl 1063.81626 · doi:10.4310/ATMP.2000.v4.n3.a5 |
| [50] | Faulkner, T.; Guica, M.; Hartman, T.; Myers, R. C.; Van Raamsdonk, M., Gravitation from entanglement in holographic CFTs, J. High Energy Phys., JHEP03(2014), 051, (2014) · Zbl 1333.83141 · doi:10.1007/JHEP03(2014)051 |
| [51] | Hung, L-Y; Myers, R. C.; Smolkin, M.; Yale, A., Holographic calculations of Renyi entropy, J. High Energy Phys., JHEP12(2011), 047, (2011) · Zbl 1306.81159 · doi:10.1007/JHEP12(2011)047 |
| [52] | Epstein, H.; Glaser, V.; Jaffe, A., Nonpositivity of energy density in quantized field theories, Nuovo Cimento, 36, 1016, (1965) · doi:10.1007/BF02749799 |
| [53] | Fewster, C. J., Lectures on quantum energy inequalities, (2012) |
| [54] | Blanco, D. D.; Casini, H., Localization of negative energy and the Bekenstein bound, Phys. Rev. Lett., 111, (2013) · doi:10.1103/PhysRevLett.111.221601 |
| [55] | Bianchi, E.; Smerlak, M., Entanglement entropy and negative energy in two dimensions, Phys. Rev. D, 90, (2014) · doi:10.1103/PhysRevD.90.041904 |
| [56] | Blanco, D.; Casini, H.; Leston, M.; Rosso, F., Modular energy inequalities from relative entropy, J. High Energy Phys., JHEP01(2018), 154, (2018) · Zbl 1384.81092 · doi:10.1007/JHEP01(2018)154 |
| [57] | Johnson, C. V., An exact efficiency formula for holographic heat engines, Entropy, 18, 120, (2016) · doi:10.3390/e18040120 |
| [58] | Chakraborty, A.; Johnson, C. V., Benchmarking black hole heat engines, Int. J. Mod. Phys. D, 28, 11950012, (2019) · doi:10.1142/S0218271819500123 |
| [59] | Hennigar, R. A.; McCarthy, F.; Ballon, A.; Mann, R. B., Holographic heat engines: general considerations and rotating black holes, Class. Quantum Grav., 34, (2017) · Zbl 1372.83040 · doi:10.1088/1361-6382/aa7f0f |
| [60] | Chakraborty, A.; Johnson, C. V., Benchmarking black hole heat engines, II, Int. J. Mod. Phys. D, 28, 1950006, (2019) · Zbl 1425.83022 · doi:10.1142/S0218271819500068 |
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