Abstract
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 → \( \mathcal{N} \) = 1) and in \( \mathcal{N} \) ≥ 3, d = 4 EMSGTs by decomposing them into \( \mathcal{N} \) = 2 multiplets (\( \mathcal{N} \) ≥ 3 → \( \mathcal{N} \) = 2). For completeness, we also obtain logarithmic entropy correction results for the non-extremal Kerr-Newman black holes in the matter coupled \( \mathcal{N} \) ≥ 1, d = 4 EMSGTs by employing the same Seeley-DeWitt data into a different Euclidean gravity approach developed in [17].
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References
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
S. Banerjee, R.K. Gupta and A. Sen, Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function, JHEP 03 (2011) 147 [arXiv:1005.3044] [INSPIRE].
S. Banerjee, R.K. Gupta, I. Mandal and A. Sen, Logarithmic Corrections to N = 4 and N = 8 Black Hole Entropy: A One Loop Test of Quantum Gravity, JHEP 11 (2011) 143 [arXiv:1106.0080] [INSPIRE].
A. Sen, Logarithmic Corrections to N = 2 Black Hole Entropy: An Infrared Window into the Microstates, Gen. Rel. Grav. 44 (2012) 1207 [arXiv:1108.3842] [INSPIRE].
R.K. Gupta, S. Lal and S. Thakur, Logarithmic corrections to extremal black hole entropy in \( \mathcal{N} \) = 2, 4 and 8 supergravity, JHEP 11 (2014) 072 [arXiv:1402.2441] [INSPIRE].
S. Ferrara and A. Marrani, Generalized Mirror Symmetry and Quantum Black Hole Entropy, Phys. Lett. B 707 (2012) 173 [arXiv:1109.0444] [INSPIRE].
C. Keeler, F. Larsen and P. Lisbao, Logarithmic Corrections to N ≥ 2 Black Hole Entropy, Phys. Rev. D 90 (2014) 043011 [arXiv:1404.1379] [INSPIRE].
F. Larsen and P. Lisbao, Quantum Corrections to Supergravity on AdS2 × S2, Phys. Rev. D 91 (2015) 084056 [arXiv:1411.7423] [INSPIRE].
S. Karan, G. Banerjee and B. Panda, Seeley-DeWitt Coefficients in \( \mathcal{N} \) = 2 Einstein-Maxwell Supergravity Theory and Logarithmic Corrections to \( \mathcal{N} \) = 2 Extremal Black Hole Entropy, JHEP 08 (2019) 056 [arXiv:1905.13058] [INSPIRE].
G. Banerjee, S. Karan and B. Panda, Logarithmic correction to the entropy of extremal black holes in \( \mathcal{N} \) = 1 Einstein-Maxwell supergravity, JHEP 01 (2021) 090 [arXiv:2007.11497] [INSPIRE].
A. Sen, Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions, Gen. Rel. Grav. 44 (2012) 1947 [arXiv:1109.3706] [INSPIRE].
S. Bhattacharyya, B. Panda and A. Sen, Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory, JHEP 08 (2012) 084 [arXiv:1204.4061] [INSPIRE].
A. Chowdhury, R.K. Gupta, S. Lal, M. Shyani and S. Thakur, Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function, JHEP 11 (2014) 002 [arXiv:1404.6363] [INSPIRE].
I. Jeon and S. Lal, Logarithmic Corrections to Entropy of Magnetically Charged AdS4 Black Holes, Phys. Lett. B 774 (2017) 41 [arXiv:1707.04208] [INSPIRE].
A. Sen, Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions, JHEP 04 (2013) 156 [arXiv:1205.0971] [INSPIRE].
A.M. Charles and F. Larsen, Universal corrections to non-extremal black hole entropy in \( \mathcal{N} \) ≥ 2 supergravity, JHEP 06 (2015) 200 [arXiv:1505.01156] [INSPIRE].
A. Castro, V. Godet, F. Larsen and Y. Zeng, Logarithmic Corrections to Black Hole Entropy: the Non-BPS Branch, JHEP 05 (2018) 079 [arXiv:1801.01926] [INSPIRE].
T. Mohaupt, Black hole entropy, special geometry and strings, Fortsch. Phys. 49 (2001) 3 [hep-th/0007195] [INSPIRE].
A. Sen, Entropy Function and AdS2/CFT1 Correspondence, JHEP 11 (2008) 075 [arXiv:0805.0095] [INSPIRE].
A. Sen, Quantum Entropy Function from AdS2/CFT1 Correspondence, Int. J. Mod. Phys. A 24 (2009) 4225 [arXiv:0809.3304] [INSPIRE].
A. Sen, Arithmetic of Quantum Entropy Function, JHEP 08 (2009) 068 [arXiv:0903.1477] [INSPIRE].
S.N. Solodukhin, The Conical singularity and quantum corrections to entropy of black hole, Phys. Rev. D 51 (1995) 609 [hep-th/9407001] [INSPIRE].
S.N. Solodukhin, On ‘Nongeometric’ contribution to the entropy of black hole due to quantum corrections, Phys. Rev. D 51 (1995) 618 [hep-th/9408068] [INSPIRE].
D.V. Fursaev, Temperature and entropy of a quantum black hole and conformal anomaly, Phys. Rev. D 51 (1995) 5352 [hep-th/9412161] [INSPIRE].
N.E. Mavromatos and E. Winstanley, Aspects of hairy black holes in spontaneously broken Einstein Yang-Mills systems: Stability analysis and entropy considerations, Phys. Rev. D 53 (1996) 3190 [hep-th/9510007] [INSPIRE].
R.B. Mann and S.N. Solodukhin, Conical geometry and quantum entropy of a charged Kerr black hole, Phys. Rev. D 54 (1996) 3932 [hep-th/9604118] [INSPIRE].
R.B. Mann and S.N. Solodukhin, Universality of quantum entropy for extreme black holes, Nucl. Phys. B 523 (1998) 293 [hep-th/9709064] [INSPIRE].
R.K. Kaul and P. Majumdar, Logarithmic correction to the Bekenstein-Hawking entropy, Phys. Rev. Lett. 84 (2000) 5255 [gr-qc/0002040] [INSPIRE].
S. Carlip, Logarithmic corrections to black hole entropy from the Cardy formula, Class. Quant. Grav. 17 (2000) 4175 [gr-qc/0005017] [INSPIRE].
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].
K.S. Gupta and S. Sen, Further evidence for the conformal structure of a Schwarzschild black hole in an algebraic approach, Phys. Lett. B 526 (2002) 121 [hep-th/0112041] [INSPIRE].
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].
D.N. Page, Hawking radiation and black hole thermodynamics, New J. Phys. 7 (2005) 203 [hep-th/0409024] [INSPIRE].
R. Banerjee and B.R. Majhi, Quantum Tunneling Beyond Semiclassical Approximation, JHEP 06 (2008) 095 [arXiv:0805.2220] [INSPIRE].
R. Banerjee and B.R. Majhi, Quantum Tunneling, Trace Anomaly and Effective Metric, Phys. Lett. B 674 (2009) 218 [arXiv:0808.3688] [INSPIRE].
B.R. Majhi, Fermion Tunneling Beyond Semiclassical Approximation, Phys. Rev. D 79 (2009) 044005 [arXiv:0809.1508] [INSPIRE].
R.-G. Cai, L.-M. Cao and N. Ohta, Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy, JHEP 04 (2010) 082 [arXiv:0911.4379] [INSPIRE].
R. Aros, D.E. Diaz and A. Montecinos, Logarithmic correction to BH entropy as Noether charge, JHEP 07 (2010) 012 [arXiv:1003.1083] [INSPIRE].
S.N. Solodukhin, Entanglement entropy of round spheres, Phys. Lett. B 693 (2010) 605 [arXiv:1008.4314] [INSPIRE].
A. Dabholkar, J. Gomes and S. Murthy, Quantum black holes, localization and the topological string, JHEP 06 (2011) 019 [arXiv:1012.0265] [INSPIRE].
A. Dabholkar, J. Gomes and S. Murthy, Localization & Exact Holography, JHEP 04 (2013) 062 [arXiv:1111.1161] [INSPIRE].
R.K. Gupta and S. Murthy, All solutions of the localization equations for N = 2 quantum black hole entropy, JHEP 02 (2013) 141 [arXiv:1208.6221] [INSPIRE].
A. Dabholkar, J. Gomes and S. Murthy, Nonperturbative black hole entropy and Kloosterman sums, JHEP 03 (2015) 074 [arXiv:1404.0033] [INSPIRE].
S. Murthy and V. Reys, Functional determinants, index theorems, and exact quantum black hole entropy, JHEP 12 (2015) 028 [arXiv:1504.01400] [INSPIRE].
R.K. Gupta, Y. Ito and I. Jeon, Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets, JHEP 11 (2015) 197 [arXiv:1504.01700] [INSPIRE].
S. Murthy and V. Reys, Single-centered black hole microstate degeneracies from instantons in supergravity, JHEP 04 (2016) 052 [arXiv:1512.01553] [INSPIRE].
B.S. DeWitt, Dynamical theory of groups and fields, Gordon and Breach, New York, U.S.A. (1965).
B.S. DeWitt, Quantum Theory of Gravity. 1. The Canonical Theory, Phys. Rev. 160 (1967) 1113 [INSPIRE].
B.S. DeWitt, Quantum Theory of Gravity. 2. The Manifestly Covariant Theory, Phys. Rev. 162 (1967) 1195 [INSPIRE].
B.S. DeWitt, Quantum Theory of Gravity. 3. Applications of the Covariant Theory, Phys. Rev. 162 (1967) 1239 [INSPIRE].
R.T. Seeley, Singular integrals and boundary value problems, Amer. J. Math. 88 (1966) 781.
R. Seeley, The resolvent of an elliptic boundary value problem, Amer. J. Math. 91 (1969) 889.
D.V. Vassilevich, Heat kernel expansion: User’s manual, Phys. Rept. 388 (2003) 279 [hep-th/0306138] [INSPIRE].
F. Denef, S.A. Hartnoll and S. Sachdev, Black hole determinants and quasinormal modes, Class. Quant. Grav. 27 (2010) 125001 [arXiv:0908.2657] [INSPIRE].
J.R. David, M.R. Gaberdiel and R. Gopakumar, The Heat Kernel on AdS3 and its Applications, JHEP 04 (2010) 125 [arXiv:0911.5085] [INSPIRE].
R. Gopakumar, R.K. Gupta and S. Lal, The Heat Kernel on AdS, JHEP 11 (2011) 010 [arXiv:1103.3627] [INSPIRE].
I. Lovrekovic, One loop partition function of six dimensional conformal gravity using heat kernel on AdS, JHEP 10 (2016) 064 [arXiv:1512.00858] [INSPIRE].
I. Mandal and A. Sen, Black Hole Microstate Counting and its Macroscopic Counterpart, Class. Quant. Grav. 27 (2010) 214003 [arXiv:1008.3801] [INSPIRE].
A. Sen, Microscopic and Macroscopic Entropy of Extremal Black Holes in String Theory, Gen. Rel. Grav. 46 (2014) 1711 [arXiv:1402.0109] [INSPIRE].
M. Gra na, Flux compactifications in string theory: A Comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge, U.K. (2012) [DOI].
T. Adamo and E.T. Newman, The Kerr-Newman metric: A Review, Scholarpedia 9 (2014) 31791 [arXiv:1410.6626] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
S.W. Hawking, Quantum Gravity and Path Integrals, Phys. Rev. D 18 (1978) 1747 [INSPIRE].
S.W. Hawking, Zeta Function Regularization of Path Integrals in Curved Space-Time, Commun. Math. Phys. 55 (1977) 133 [INSPIRE].
G. Denardo and E. Spallucci, Induced Quantum Gravity From Heat Kernel Expansion, Nuovo Cim. A 69 (1982) 151 [INSPIRE].
I.G. Avramidi, The Heat kernel approach for calculating the effective action in quantum field theory and quantum gravity, hep-th/9509077 [INSPIRE].
G. De Berredo-Peixoto, A Note on the heat kernel method applied to fermions, Mod. Phys. Lett. A 16 (2001) 2463 [hep-th/0108223] [INSPIRE].
J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664 [INSPIRE].
B.S. DeWitt, Quantum Field Theory in Curved Space-Time, Phys. Rept. 19 (1975) 295 [INSPIRE].
S. Karan, S. Kumar and B. Panda, General heat kernel coefficients for massless free spin-3/2 Rarita-Schwinger field, Int. J. Mod. Phys. A 33 (2018) 1850063 [arXiv:1709.08063] [INSPIRE].
R.C. Henry, Kretschmann scalar for a Kerr-Newman black hole, Astrophys. J. 535 (2000) 350 [astro-ph/9912320] [INSPIRE].
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. D 11 (2002) 827 [gr-qc/0302095] [INSPIRE].
J.D. Bekenstein, Bekenstein-Hawking entropy, Scholarpedia 3 (2008) 7375.
L. Andrianopoli, R. D’Auria, S. Ferrara and M. Trigiante, Black-hole attractors in N = 1 supergravity, JHEP 07 (2007) 019 [hep-th/0703178] [INSPIRE].
L. Andrianopoli, R. D’Auria and S. Ferrara, Consistent reduction of N = 2 → N = 1 four-dimensional supergravity coupled to matter, Nucl. Phys. B 628 (2002) 387 [hep-th/0112192] [INSPIRE].
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Karan, S., Panda, B. Logarithmic corrections to black hole entropy in matter coupled \( \mathcal{N} \) ≥ 1 Einstein-Maxwell supergravity. J. High Energ. Phys. 2021, 104 (2021). https://doi.org/10.1007/JHEP05(2021)104
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DOI: https://doi.org/10.1007/JHEP05(2021)104