Logarithmic corrections to black hole entropy in matter coupled \(\mathcal{N} \geq 1\) Einstein-Maxwell supergravity. (English) Zbl 1466.83137
Summary: We calculate the first three Seeley-DeWitt coefficients for fluctuation of the massless fields of a \(\mathcal{N} = 2\) Einstein-Maxwell supergravity theory (EMSGT) distributed into different multiplets in \(d = 4\) space-time dimensions. By utilizing the Seeley-DeWitt data in the quantum entropy function formalism, we then obtain the logarithmic correction contribution of individual multiplets to the entropy of extremal Kerr-Newman family of black holes. Our results allow us to find the logarithmic entropy corrections for the extremal black holes in a fully matter coupled \(\mathcal{N} = 2 \), \(d = 4\) EMSGT, in a particular class of \(\mathcal{N} = 1\), \(d = 4\) EMSGT as consistent decomposition of \(\mathcal{N} = 2\) multiplets \(( \mathcal{N} = 2 \rightarrow \mathcal{N} = 1)\) and in \(\mathcal{N} \geq 3 \), \(d = 4\) EMSGTs by decomposing them into \(\mathcal{N} = 2\) multiplets \(( \mathcal{N} \geq 3 \rightarrow \mathcal{N} = 2)\). For completeness, we also obtain logarithmic entropy correction results for the non-extremal Kerr-Newman black holes in the matter coupled \(\mathcal{N} \geq 1 \), \(d = 4\) EMSGTs by employing the same Seeley-DeWitt data into a different Euclidean gravity approach developed in [A. Sen, J. High Energy Phys. 2013, No. 4, Paper No. 156, 33 p. (2013; Zbl 1342.83207)].
MSC:
| 83E50 | Supergravity |
| 83C22 | Einstein-Maxwell equations |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 83C57 | Black holes |
| 81P17 | Quantum entropies |
Citations:
Zbl 1342.83207References:
| [1] | Bekenstein, JD, Black holes and entropy, Phys. Rev. D, 7, 2333 (1973) · Zbl 1369.83037 · doi:10.1103/PhysRevD.7.2333 |
| [2] | S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys.43 (1975) 199 [Erratum ibid.46 (1976) 206] [INSPIRE]. · Zbl 1378.83040 |
| [3] | R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D48 (1993) R3427 [gr-qc/9307038] [INSPIRE]. · Zbl 0942.83512 |
| [4] | Banerjee, S.; Gupta, RK; Sen, A., Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function, JHEP, 03, 147 (2011) · Zbl 1301.81182 · doi:10.1007/JHEP03(2011)147 |
| [5] | Banerjee, S.; Gupta, RK; Mandal, I.; Sen, A., Logarithmic Corrections to N = 4 and N = 8 Black Hole Entropy: A One Loop Test of Quantum Gravity, JHEP, 11, 143 (2011) · Zbl 1306.83038 · doi:10.1007/JHEP11(2011)143 |
| [6] | Sen, A., Logarithmic Corrections to N = 2 Black Hole Entropy: An Infrared Window into the Microstates, Gen. Rel. Grav., 44, 1207 (2012) · Zbl 1241.83051 · doi:10.1007/s10714-012-1336-5 |
| [7] | Gupta, RK; Lal, S.; Thakur, S., Logarithmic corrections to extremal black hole entropy in \(\mathcal{N} = 2, 4\) and 8 supergravity, JHEP, 11, 072 (2014) · Zbl 1333.83086 · doi:10.1007/JHEP11(2014)072 |
| [8] | Ferrara, S.; Marrani, A., Generalized Mirror Symmetry and Quantum Black Hole Entropy, Phys. Lett. B, 707, 173 (2012) · doi:10.1016/j.physletb.2011.12.005 |
| [9] | Keeler, C.; Larsen, F.; Lisbao, P., Logarithmic Corrections to N ≥ 2 Black Hole Entropy, Phys. Rev. D, 90, 043011 (2014) · doi:10.1103/PhysRevD.90.043011 |
| [10] | Larsen, F.; Lisbao, P., Quantum Corrections to Supergravity on AdS_2 × S^2, Phys. Rev. D, 91, 084056 (2015) · doi:10.1103/PhysRevD.91.084056 |
| [11] | Karan, S.; Banerjee, G.; Panda, B., Seeley-DeWitt Coefficients in \(\mathcal{N} = 2\) Einstein-Maxwell Supergravity Theory and Logarithmic Corrections to \(\mathcal{N} = 2\) Extremal Black Hole Entropy, JHEP, 08, 056 (2019) · Zbl 1421.83133 · doi:10.1007/JHEP08(2019)056 |
| [12] | Banerjee, G.; Karan, S.; Panda, B., Logarithmic correction to the entropy of extremal black holes in \(\mathcal{N} = 1\) Einstein-Maxwell supergravity, JHEP, 01, 090 (2021) · Zbl 1459.83065 · doi:10.1007/JHEP01(2021)090 |
| [13] | Sen, A., Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions, Gen. Rel. Grav., 44, 1947 (2012) · Zbl 1253.83003 · doi:10.1007/s10714-012-1373-0 |
| [14] | Bhattacharyya, S.; Panda, B.; Sen, A., Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory, JHEP, 08, 084 (2012) · Zbl 1397.83052 · doi:10.1007/JHEP08(2012)084 |
| [15] | Chowdhury, A.; Gupta, RK; Lal, S.; Shyani, M.; Thakur, S., Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function, JHEP, 11, 002 (2014) · Zbl 1333.83218 · doi:10.1007/JHEP11(2014)002 |
| [16] | Jeon, I.; Lal, S., Logarithmic Corrections to Entropy of Magnetically Charged AdS4 Black Holes, Phys. Lett. B, 774, 41 (2017) · Zbl 1403.83050 · doi:10.1016/j.physletb.2017.09.026 |
| [17] | Sen, A., Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions, JHEP, 04, 156 (2013) · Zbl 1342.83207 · doi:10.1007/JHEP04(2013)156 |
| [18] | Charles, AM; Larsen, F., Universal corrections to non-extremal black hole entropy in \(\mathcal{N} \) ≥ 2 supergravity, JHEP, 06, 200 (2015) · Zbl 1388.83771 · doi:10.1007/JHEP06(2015)200 |
| [19] | Castro, A.; Godet, V.; Larsen, F.; Zeng, Y., Logarithmic Corrections to Black Hole Entropy: the Non-BPS Branch, JHEP, 05, 079 (2018) · Zbl 1391.83103 · doi:10.1007/JHEP05(2018)079 |
| [20] | Mohaupt, T., Black hole entropy, special geometry and strings, Fortsch. Phys., 49, 3 (2001) · Zbl 0985.83001 · doi:10.1002/1521-3978(200102)49:1/3<3::AID-PROP3>3.0.CO;2-# |
| [21] | Sen, A., Entropy Function and AdS_2/CFT_1Correspondence, JHEP, 11, 075 (2008) · doi:10.1088/1126-6708/2008/11/075 |
| [22] | Sen, A., Quantum Entropy Function from AdS_2/CFT_1Correspondence, Int. J. Mod. Phys. A, 24, 4225 (2009) · Zbl 1175.83045 · doi:10.1142/S0217751X09045893 |
| [23] | Sen, A., Arithmetic of Quantum Entropy Function, JHEP, 08, 068 (2009) · doi:10.1088/1126-6708/2009/08/068 |
| [24] | Solodukhin, SN, The Conical singularity and quantum corrections to entropy of black hole, Phys. Rev. D, 51, 609 (1995) · doi:10.1103/PhysRevD.51.609 |
| [25] | Solodukhin, SN, On ‘Nongeometric’ contribution to the entropy of black hole due to quantum corrections, Phys. Rev. D, 51, 618 (1995) · doi:10.1103/PhysRevD.51.618 |
| [26] | Fursaev, DV, Temperature and entropy of a quantum black hole and conformal anomaly, Phys. Rev. D, 51, 5352 (1995) · doi:10.1103/PhysRevD.51.R5352 |
| [27] | Mavromatos, NE; Winstanley, E., Aspects of hairy black holes in spontaneously broken Einstein Yang-Mills systems: Stability analysis and entropy considerations, Phys. Rev. D, 53, 3190 (1996) · doi:10.1103/PhysRevD.53.3190 |
| [28] | Mann, RB; Solodukhin, SN, Conical geometry and quantum entropy of a charged Kerr black hole, Phys. Rev. D, 54, 3932 (1996) · doi:10.1103/PhysRevD.54.3932 |
| [29] | Mann, RB; Solodukhin, SN, Universality of quantum entropy for extreme black holes, Nucl. Phys. B, 523, 293 (1998) · Zbl 0953.83015 · doi:10.1016/S0550-3213(98)00094-7 |
| [30] | R.K. Kaul and P. Majumdar, Logarithmic correction to the Bekenstein-Hawking entropy, Phys. Rev. Lett.84 (2000) 5255 [gr-qc/0002040] [INSPIRE]. |
| [31] | S. Carlip, Logarithmic corrections to black hole entropy from the Cardy formula, Class. Quant. Grav.17 (2000) 4175 [gr-qc/0005017] [INSPIRE]. · Zbl 0970.83026 |
| [32] | T.R. Govindarajan, R.K. Kaul and V. Suneeta, Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole, Class. Quant. Grav.18 (2001) 2877 [gr-qc/0104010] [INSPIRE]. · Zbl 0999.83031 |
| [33] | Gupta, KS; Sen, S., Further evidence for the conformal structure of a Schwarzschild black hole in an algebraic approach, Phys. Lett. B, 526, 121 (2002) · Zbl 0981.83030 · doi:10.1016/S0370-2693(01)01501-5 |
| [34] | A.J.M. Medved, A Comment on black hole entropy or does nature abhor a logarithm?, Class. Quant. Grav.22 (2005) 133 [gr-qc/0406044] [INSPIRE]. · Zbl 1060.83522 |
| [35] | Page, DN, Hawking radiation and black hole thermodynamics, New J. Phys., 7, 203 (2005) · doi:10.1088/1367-2630/7/1/203 |
| [36] | Banerjee, R.; Majhi, BR, Quantum Tunneling Beyond Semiclassical Approximation, JHEP, 06, 095 (2008) · doi:10.1088/1126-6708/2008/06/095 |
| [37] | Banerjee, R.; Majhi, BR, Quantum Tunneling, Trace Anomaly and Effective Metric, Phys. Lett. B, 674, 218 (2009) · doi:10.1016/j.physletb.2009.03.019 |
| [38] | Majhi, BR, Fermion Tunneling Beyond Semiclassical Approximation, Phys. Rev. D, 79, 044005 (2009) · doi:10.1103/PhysRevD.79.044005 |
| [39] | Cai, R-G; Cao, L-M; Ohta, N., Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy, JHEP, 04, 082 (2010) · Zbl 1272.83042 · doi:10.1007/JHEP04(2010)082 |
| [40] | Aros, R.; Diaz, DE; Montecinos, A., Logarithmic correction to BH entropy as Noether charge, JHEP, 07, 012 (2010) · Zbl 1290.83031 · doi:10.1007/JHEP07(2010)012 |
| [41] | Solodukhin, SN, Entanglement entropy of round spheres, Phys. Lett. B, 693, 605 (2010) · doi:10.1016/j.physletb.2010.09.018 |
| [42] | Dabholkar, A.; Gomes, J.; Murthy, S., Quantum black holes, localization and the topological string, JHEP, 06, 019 (2011) · Zbl 1298.81261 · doi:10.1007/JHEP06(2011)019 |
| [43] | Dabholkar, A.; Gomes, J.; Murthy, S., Localization & Exact Holography, JHEP, 04, 062 (2013) · Zbl 1342.81415 · doi:10.1007/JHEP04(2013)062 |
| [44] | Gupta, RK; Murthy, S., All solutions of the localization equations for N = 2 quantum black hole entropy, JHEP, 02, 141 (2013) · Zbl 1342.83027 · doi:10.1007/JHEP02(2013)141 |
| [45] | Dabholkar, A.; Gomes, J.; Murthy, S., Nonperturbative black hole entropy and Kloosterman sums, JHEP, 03, 074 (2015) · Zbl 1388.83421 · doi:10.1007/JHEP03(2015)074 |
| [46] | Murthy, S.; Reys, V., Functional determinants, index theorems, and exact quantum black hole entropy, JHEP, 12, 028 (2015) · Zbl 1388.83487 |
| [47] | Gupta, RK; Ito, Y.; Jeon, I., Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets, JHEP, 11, 197 (2015) · Zbl 1388.83453 · doi:10.1007/JHEP11(2015)197 |
| [48] | Murthy, S.; Reys, V., Single-centered black hole microstate degeneracies from instantons in supergravity, JHEP, 04, 052 (2016) · Zbl 1388.83488 |
| [49] | DeWitt, BS, Dynamical theory of groups and fields (1965), New York, U.S.A.: Gordon and Breach, New York, U.S.A. · Zbl 0169.57101 |
| [50] | B.S. DeWitt, Quantum Theory of Gravity. 1. The Canonical Theory, Phys. Rev.160 (1967) 1113 [INSPIRE]. · Zbl 0158.46504 |
| [51] | B.S. DeWitt, Quantum Theory of Gravity. 2. The Manifestly Covariant Theory, Phys. Rev.162 (1967) 1195 [INSPIRE]. · Zbl 0161.46501 |
| [52] | B.S. DeWitt, Quantum Theory of Gravity. 3. Applications of the Covariant Theory, Phys. Rev.162 (1967) 1239 [INSPIRE]. · Zbl 0161.46501 |
| [53] | Seeley, RT, Singular integrals and boundary value problems, Amer. J. Math., 88, 781 (1966) · Zbl 0178.17601 · doi:10.2307/2373078 |
| [54] | Seeley, R., The resolvent of an elliptic boundary value problem, Amer. J. Math., 91, 889 (1969) · Zbl 0191.11801 · doi:10.2307/2373309 |
| [55] | Vassilevich, DV, Heat kernel expansion: User’s manual, Phys. Rept., 388, 279 (2003) · Zbl 1042.81093 · doi:10.1016/j.physrep.2003.09.002 |
| [56] | Denef, F.; Hartnoll, SA; Sachdev, S., Black hole determinants and quasinormal modes, Class. Quant. Grav., 27, 125001 (2010) · Zbl 1190.83040 · doi:10.1088/0264-9381/27/12/125001 |
| [57] | David, JR; Gaberdiel, MR; Gopakumar, R., The Heat Kernel on AdS_3and its Applications, JHEP, 04, 125 (2010) · Zbl 1272.83081 · doi:10.1007/JHEP04(2010)125 |
| [58] | Gopakumar, R.; Gupta, RK; Lal, S., The Heat Kernel on AdS, JHEP, 11, 010 (2011) · Zbl 1306.81155 · doi:10.1007/JHEP11(2011)010 |
| [59] | Lovrekovic, I., One loop partition function of six dimensional conformal gravity using heat kernel on AdS, JHEP, 10, 064 (2016) · Zbl 1390.83066 · doi:10.1007/JHEP10(2016)064 |
| [60] | Mandal, I.; Sen, A., Black Hole Microstate Counting and its Macroscopic Counterpart, Class. Quant. Grav., 27, 214003 (2010) · Zbl 1204.83004 · doi:10.1088/0264-9381/27/21/214003 |
| [61] | Sen, A., Microscopic and Macroscopic Entropy of Extremal Black Holes in String Theory, Gen. Rel. Grav., 46, 1711 (2014) · Zbl 1291.83015 · doi:10.1007/s10714-014-1711-5 |
| [62] | M. Gra na, Flux compactifications in string theory: A Comprehensive review, Phys. Rept.423 (2006) 91 [hep-th/0509003] [INSPIRE]. |
| [63] | D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge, U.K. (2012) [DOI]. · Zbl 1245.83001 |
| [64] | Adamo, T.; Newman, ET, The Kerr-Newman metric: A Review, Scholarpedia, 9, 31791 (2014) · doi:10.4249/scholarpedia.31791 |
| [65] | Gibbons, GW; Hawking, SW, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D, 15, 2752 (1977) · doi:10.1103/PhysRevD.15.2752 |
| [66] | Hawking, SW, Quantum Gravity and Path Integrals, Phys. Rev. D, 18, 1747 (1978) · doi:10.1103/PhysRevD.18.1747 |
| [67] | Hawking, SW, Zeta Function Regularization of Path Integrals in Curved Space-Time, Commun. Math. Phys., 55, 133 (1977) · Zbl 0407.58024 · doi:10.1007/BF01626516 |
| [68] | Denardo, G.; Spallucci, E., Induced Quantum Gravity From Heat Kernel Expansion, Nuovo Cim. A, 69, 151 (1982) · doi:10.1007/BF02902652 |
| [69] | I.G. Avramidi, The Heat kernel approach for calculating the effective action in quantum field theory and quantum gravity, hep-th/9509077 [INSPIRE]. · Zbl 0866.58071 |
| [70] | De Berredo-Peixoto, G., A Note on the heat kernel method applied to fermions, Mod. Phys. Lett. A, 16, 2463 (2001) · Zbl 1138.81469 · doi:10.1142/S0217732301005965 |
| [71] | Schwinger, JS, On gauge invariance and vacuum polarization, Phys. Rev., 82, 664 (1951) · Zbl 0043.42201 · doi:10.1103/PhysRev.82.664 |
| [72] | DeWitt, BS, Quantum Field Theory in Curved Space-Time, Phys. Rept., 19, 295 (1975) · doi:10.1016/0370-1573(75)90051-4 |
| [73] | Karan, S.; Kumar, S.; Panda, B., General heat kernel coefficients for massless free spin-3/2 Rarita-Schwinger field, Int. J. Mod. Phys. A, 33, 1850063 (2018) · Zbl 1387.81260 · doi:10.1142/S0217751X1850063X |
| [74] | R.C. Henry, Kretschmann scalar for a Kerr-Newman black hole, Astrophys. J.535 (2000) 350 [astro-ph/9912320] [INSPIRE]. |
| [75] | C. Cherubini, D. Bini, S. Capozziello and R. Ruffini, Second order scalar invariants of the Riemann tensor: Applications to black hole space-times, Int. J. Mod. Phys. D11 (2002) 827 [gr-qc/0302095] [INSPIRE]. · Zbl 1070.83524 |
| [76] | Bekenstein, JD, Bekenstein-Hawking entropy, Scholarpedia, 3, 7375 (2008) · doi:10.4249/scholarpedia.7375 |
| [77] | Andrianopoli, L.; D’Auria, R.; Ferrara, S.; Trigiante, M., Black-hole attractors in N = 1 supergravity, JHEP, 07, 019 (2007) · doi:10.1088/1126-6708/2007/07/019 |
| [78] | Andrianopoli, L.; D’Auria, R.; Ferrara, S., Consistent reduction of N = 2 → N = 1 four-dimensional supergravity coupled to matter, Nucl. Phys. B, 628, 387 (2002) · Zbl 0992.83086 · doi:10.1016/S0550-3213(02)00090-1 |
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