Entropy functional and the holographic attractor mechanism. (English) Zbl 1391.81150
Summary: We provide a field theory interpretation of the attractor mechanism for asymptotically \(\mathrm{AdS}_{4}\) dyonic BPS black holes whose entropy is captured by the supersymmetric index of the twisted ABJM theory at Chern-Simons level one. We holographically compute the renormalized off-shell quantum effective action in the twisted ABJM theory as a function of the supersymmetric fermion masses and the arbitrary vacuum expectation values of the dimension one scalar bilinear operators and show that extremizing the effective action with respect to the vacuum expectation values of the dimension one scalar bilinears is equivalent to the attractor mechanism in the bulk. In fact, we show that the holographic quantum effective action coincides with the entropy functional and, therefore, its value at the extremum reproduces the black hole entropy.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 83C57 | Black holes |
| 83E30 | String and superstring theories in gravitational theory |
| 94A17 | Measures of information, entropy |
| 81T60 | Supersymmetric field theories in quantum mechanics |
Keywords:
AdS-CFT correspondence; black holes in string theory; gauge-gravity correspondence; supersymmetric gauge theoryReferences:
| [1] | Maldacena, JM, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., 38, 1113, (1999) · Zbl 0969.81047 · doi:10.1023/A:1026654312961 |
| [2] | Benini, F.; Hristov, K.; Zaffaroni, A., Black hole microstates in ads_{4} from supersymmetric localization, JHEP, 05, 054, (2016) · Zbl 1388.83388 · doi:10.1007/JHEP05(2016)054 |
| [3] | Benini, F.; Hristov, K.; Zaffaroni, A., Exact microstate counting for dyonic black holes in ads4, Phys. Lett., B 771, 462, (2017) · Zbl 1372.83030 · doi:10.1016/j.physletb.2017.05.076 |
| [4] | Cabo-Bizet, A.; Giraldo-Rivera, VI; Pando Zayas, LA, Microstate counting of ads_{4} hyperbolic black hole entropy via the topologically twisted index, JHEP, 08, 023, (2017) · Zbl 1381.83055 · doi:10.1007/JHEP08(2017)023 |
| [5] | Azzurli, F.; Bobev, N.; Crichigno, PM; Min, VS; Zaffaroni, A., A universal counting of black hole microstates in ads_{4}, JHEP, 02, 054, (2018) · Zbl 1387.81303 · doi:10.1007/JHEP02(2018)054 |
| [6] | F. Benini, H. Khachatryan and P. Milan, Black hole entropy in massive Type IIA, Class. Quant. Grav.35 (2018) 035004 [arXiv:1707.06886] [INSPIRE]. · Zbl 1382.83040 |
| [7] | Hosseini, SM; Hristov, K.; Passias, A., Holographic microstate counting for ads_{4} black holes in massive IIA supergravity, JHEP, 10, 190, (2017) · Zbl 1383.83212 · doi:10.1007/JHEP10(2017)190 |
| [8] | S. Ferrara, R. Kallosh and A. Strominger, \(N\) = 2 extremal black holes, Phys. Rev.D 52 (1995) R5412 [hep-th/9508072] [INSPIRE]. · Zbl 1384.81111 |
| [9] | Strominger, A., Macroscopic entropy of N = 2 extremal black holes, Phys. Lett., B 383, 39, (1996) · doi:10.1016/0370-2693(96)00711-3 |
| [10] | Ferrara, S.; Kallosh, R., Supersymmetry and attractors, Phys. Rev., D 54, 1514, (1996) · Zbl 1171.83329 |
| [11] | Sen, A., Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP, 09, 038, (2005) · doi:10.1088/1126-6708/2005/09/038 |
| [12] | S. Dutta and R. Gopakumar, On Euclidean and Noetherian entropies in AdS space, Phys. Rev.D 74 (2006) 044007 [hep-th/0604070] [INSPIRE]. · Zbl 1388.83388 |
| [13] | Lindgren, J.; Papadimitriou, I.; Taliotis, A.; Vanhoof, J., Holographic Hall conductivities from dyonic backgrounds, JHEP, 07, 094, (2015) · Zbl 1388.83294 · doi:10.1007/JHEP07(2015)094 |
| [14] | M.J. Duff and J.T. Liu, Anti-de Sitter black holes in gauged N = 8 supergravity, Nucl. Phys.B 554 (1999) 237 [hep-th/9901149] [INSPIRE]. · Zbl 0951.83060 |
| [15] | M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys.B 558 (1999) 96 [hep-th/9903214] [INSPIRE]. · Zbl 1388.81400 |
| [16] | Dall’Agata, G.; Gnecchi, A., Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity, JHEP, 03, 037, (2011) · Zbl 1301.81248 · doi:10.1007/JHEP03(2011)037 |
| [17] | Klemm, D.; Petri, N.; Rabbiosi, M., Symplectically invariant flow equations for N = 2, D=4 gauged supergravity with hypermultiplets, JHEP, 04, 008, (2016) · Zbl 1388.83676 |
| [18] | Hristov, K.; Vandoren, S., static supersymmetric black holes in AdS_{4}with spherical symmetry, JHEP, 04, 047, (2011) · Zbl 1250.83041 · doi:10.1007/JHEP04(2011)047 |
| [19] | Ceresole, A.; Dall’Agata, G., Flow equations for non-BPS extremal black holes, JHEP, 03, 110, (2007) · doi:10.1088/1126-6708/2007/03/110 |
| [20] | Andrianopoli, L.; D’Auria, R.; Orazi, E.; Trigiante, M., First order description of black holes in moduli space, JHEP, 11, 032, (2007) · Zbl 1245.83021 · doi:10.1088/1126-6708/2007/11/032 |
| [21] | L. Andrianopoli, R. D’Auria, E. Orazi and M. Trigiante, First Order Description of D = 4 static Black Holes and the Hamilton-Jacobi equation, Nucl. Phys.B 833 (2010) 1 [arXiv:0905.3938] [INSPIRE]. · Zbl 1204.83091 |
| [22] | Trigiante, M.; Riet, T.; Vercnocke, B., Fake supersymmetry versus Hamilton-Jacobi, JHEP, 05, 078, (2012) · Zbl 1348.81386 · doi:10.1007/JHEP05(2012)078 |
| [23] | A. Gnecchi and C. Toldo, On the non-BPS first order flow in N = 2 U(1)-gauged Supergravity, JHEP03 (2013) 088 [arXiv:1211.1966] [INSPIRE]. · Zbl 1342.83475 |
| [24] | Gnecchi, A.; Toldo, C., First order flow for non-extremal AdS black holes and mass from holographic renormalization, JHEP, 10, 075, (2014) · Zbl 1333.83081 · doi:10.1007/JHEP10(2014)075 |
| [25] | Klemm, D.; Rabbiosi, M., First order flow equations for nonextremal black holes in AdS (super)gravity, JHEP, 10, 149, (2017) · Zbl 1383.83215 · doi:10.1007/JHEP10(2017)149 |
| [26] | Kiritsis, E.; Niarchos, V., The holographic quantum effective potential at finite temperature and density, JHEP, 08, 164, (2012) · doi:10.1007/JHEP08(2012)164 |
| [27] | G.W. Gibbons and R.E. Kallosh, Topology, entropy and Witten index of dilaton black holes, Phys. Rev.D 51 (1995) 2839 [hep-th/9407118] [INSPIRE]. · Zbl 1298.81194 |
| [28] | Carroll, SM; Johnson, MC; Randall, L., Extremal limits and black hole entropy, JHEP, 11, 109, (2009) · doi:10.1088/1126-6708/2009/11/109 |
| [29] | Sen, A., Entropy function and ads_{2}/CF T_{1} correspondence, JHEP, 11, 075, (2008) · doi:10.1088/1126-6708/2008/11/075 |
| [30] | Almheiri, A.; Kang, B., Conformal symmetry breaking and thermodynamics of near-extremal black holes, JHEP, 10, 052, (2016) · Zbl 1390.83167 · doi:10.1007/JHEP10(2016)052 |
| [31] | Papadimitriou, I., Holographic renormalization of general Dilaton-axion gravity, JHEP, 08, 119, (2011) · Zbl 1298.81194 · doi:10.1007/JHEP08(2011)119 |
| [32] | An, OS, Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization, JHEP, 12, 107, (2017) · Zbl 1383.81174 · doi:10.1007/JHEP12(2017)107 |
| [33] | Breitenlohner, P.; Freedman, DZ, Positive energy in anti-de Sitter backgrounds and gauged extended supergravity, Phys. Lett., 115B, 197, (1982) · doi:10.1016/0370-2693(82)90643-8 |
| [34] | Freedman, DZ; Pufu, SS, The holography of F -maximization, JHEP, 03, 135, (2014) · Zbl 1333.83235 · doi:10.1007/JHEP03(2014)135 |
| [35] | Papadimitriou, I., Multi-trace deformations in AdS/CFT: exploring the vacuum structure of the deformed CFT, JHEP, 05, 075, (2007) · doi:10.1088/1126-6708/2007/05/075 |
| [36] | Caldarelli, MM; Christodoulou, A.; Papadimitriou, I.; Skenderis, K., Phases of planar AdS black holes with axionic charge, JHEP, 04, 001, (2017) · Zbl 1378.83031 · doi:10.1007/JHEP04(2017)001 |
| [37] | Papadimitriou, I.; Skenderis, K., Correlation functions in holographic RG flows, JHEP, 10, 075, (2004) · doi:10.1088/1126-6708/2004/10/075 |
| [38] | Freedman, DZ; Pilch, K.; Pufu, SS; Warner, NP, Boundary terms and three-point functions: an AdS/CFT puzzle resolved, JHEP, 06, 053, (2017) · Zbl 1380.81316 · doi:10.1007/JHEP06(2017)053 |
| [39] | Halmagyi, N.; Lal, S., On the on-shell: the action of ads_{4} black holes, JHEP, 03, 146, (2018) · Zbl 1388.83662 · doi:10.1007/JHEP03(2018)146 |
| [40] | S. de Haro, I. Papadimitriou and A.C. Petkou, Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS_{4}, Phys. Rev. Lett.98 (2007) 231601 [hep-th/0611315] [INSPIRE]. · Zbl 1250.83041 |
| [41] | Kiritsis, E.; Li, W.; Nitti, F., Holographic RG flow and the quantum effective action, Fortsch. Phys., 62, 389, (2014) · Zbl 1338.81275 · doi:10.1002/prop.201400007 |
| [42] | Papadimitriou, I.; Skenderis, K., Thermodynamics of asymptotically locally AdS spacetimes, JHEP, 08, 004, (2005) · doi:10.1088/1126-6708/2005/08/004 |
| [43] | Cacciatori, SL; Klemm, D., Supersymmetric ads_{4} black holes and attractors, JHEP, 01, 085, (2010) · Zbl 1269.81110 · doi:10.1007/JHEP01(2010)085 |
| [44] | Benini, F.; Zaffaroni, A., A topologically twisted index for three-dimensional supersymmetric theories, JHEP, 07, 127, (2015) · Zbl 1388.81400 · doi:10.1007/JHEP07(2015)127 |
| [45] | Halmagyi, N., Static BPS black holes in ads_{4} with general dyonic charges, JHEP, 03, 032, (2015) · doi:10.1007/JHEP03(2015)032 |
| [46] | Goulart, P., Dyonic ads_{4} black hole entropy and attractors via entropy function, JHEP, 09, 003, (2016) · Zbl 1390.83200 · doi:10.1007/JHEP09(2016)003 |
| [47] | Papadimitriou, I., Supercurrent anomalies in 4d scfts, JHEP, 07, 038, (2017) · Zbl 1380.81354 · doi:10.1007/JHEP07(2017)038 |
| [48] | Benetti Genolini, P.; Cassani, D.; Martelli, D.; Sparks, J., Holographic renormalization and supersymmetry, JHEP, 02, 132, (2017) · Zbl 1377.81201 · doi:10.1007/JHEP02(2017)132 |
| [49] | A. Sen, Quantum Entropy Function from AdS_{2}/CF T_{1}Correspondence, Int. J. Mod. Phys.A 24 (2009) 4225 [arXiv:0809.3304] [INSPIRE]. · Zbl 1175.83045 |
| [50] | Liu, JT; Pando Zayas, LA; Rathee, V.; Zhao, W., Toward microstate counting beyond large N in localization and the dual one-loop quantum supergravity, JHEP, 01, 026, (2018) · Zbl 1384.81111 · doi:10.1007/JHEP01(2018)026 |
| [51] | Jeon, I.; Lal, S., Logarithmic corrections to entropy of magnetically charged ads_{4} black holes, Phys. Lett., B 774, 41, (2017) · Zbl 1403.83050 · doi:10.1016/j.physletb.2017.09.026 |
| [52] | J.T. Liu, L.A. Pando Zayas, V. Rathee and W. Zhao, A One-loop Test of Quantum Black Holes in Anti de Sitter Space, arXiv:1711.01076 [INSPIRE]. · Zbl 1381.83055 |
| [53] | Papadimitriou, I., Non-supersymmetric membrane flows from fake supergravity an multi-trace deformations, JHEP, 02, 008, (2007) · doi:10.1088/1126-6708/2007/02/008 |
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