Abstract
In a recent paper [arXiv:2308.00038], Anupam, Chowdhury, and Sen conjectured that the finite temperature Euclidean five-dimensional Cvetic-Youm solution saturating the BPS bound is supersymmetric. In this paper, we explicitly construct Killing spinors for this solution in five-dimensional minimal supergravity. We also expand on the previous discussions of Killing spinors for the finite temperature Euclidean Kerr-Newman solution saturating the BPS bound. For both these cases, we show that the total charge gets divided into two harmonic sources on three-dimensional flat base space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
A. Sen, Black Hole Entropy Function, Attractors and Precision Counting of Microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].
A. Sen, How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?, Gen. Rel. Grav. 43 (2011) 2171 [arXiv:1008.4209] [INSPIRE].
K. Bringmann and S. Murthy, On the positivity of black hole degeneracies in string theory, Commun. Num. Theor Phys. 07 (2013) 15 [arXiv:1208.3476] [INSPIRE].
A. Chattopadhyaya and J.R. David, Dyon degeneracies from Mathieu moonshine symmetry, Phys. Rev. D 96 (2017) 086020 [arXiv:1704.00434] [INSPIRE].
S. Govindarajan, S. Samanta, P. Shanmugapriya and A. Virmani, Positivity of discrete information for CHL black holes, Nucl. Phys. B 987 (2023) 116095 [arXiv:2205.08726] [INSPIRE].
A. Sen, Quantum Entropy Function from AdS2/CFT1 Correspondence, Int. J. Mod. Phys. A 24 (2009) 4225 [arXiv:0809.3304] [INSPIRE].
A. Sen, Revisiting localization for BPS black hole entropy, arXiv:2302.13490 [INSPIRE].
A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes, JHEP 10 (2019) 062 [arXiv:1810.11442] [INSPIRE].
M. Heydeman, L.V. Iliesiu, G.J. Turiaci and W. Zhao, The statistical mechanics of near-BPS black holes, J. Phys. A 55 (2022) 014004 [arXiv:2011.01953] [INSPIRE].
L.V. Iliesiu, M. Kologlu and G.J. Turiaci, Supersymmetric indices factorize, JHEP 05 (2023) 032 [arXiv:2107.09062] [INSPIRE].
L.V. Iliesiu, S. Murthy and G.J. Turiaci, Black hole microstate counting from the gravitational path integral, arXiv:2209.13602 [INSPIRE].
N. Banerjee and M. Saha, Revisiting leading quantum corrections to near extremal black hole thermodynamics, JHEP 07 (2023) 010 [arXiv:2303.12415] [INSPIRE].
A.A. H., P.V. Athira, C. Chowdhury and A. Sen, Logarithmic Correction to BPS Black Hole Entropy from Supersymmetric Index at Finite Temperature, arXiv:2306.07322 [INSPIRE].
A.H. Anupam, C. Chowdhury and A. Sen, Revisiting Logarithmic Correction to Five Dimensional BPS Black Hole Entropy, arXiv:2308.00038 [INSPIRE].
Y. Chen and G.J. Turiaci, Spin-Statistics for Black Hole Microstates, arXiv:2309.03478 [INSPIRE].
D. Kapec, A. Sheta, A. Strominger and C. Toldo, Logarithmic Corrections to Kerr Thermodynamics, arXiv:2310.00848 [INSPIRE].
I. Rakic, M. Rangamani and G.J. Turiaci, Thermodynamics of the near-extremal Kerr spacetime, arXiv:2310.04532 [INSPIRE].
J. Boruch, L.V. Iliesiu, S. Murthy and G.J. Turiaci, New forms of attraction: Attractor saddles for the black hole index, arXiv:2310.07763 [INSPIRE].
S. Mondal, Statistical Mechanics of Exponentially Many Low Lying States, arXiv:2310.12264 [INSPIRE].
N. Bobev, A.M. Charles and V.S. Min, Euclidean black saddles and AdS4 black holes, JHEP 10 (2020) 073 [arXiv:2006.01148] [INSPIRE].
Z. Perjes, Solutions of the coupled Einstein Maxwell equations representing the fields of spinning sources, Phys. Rev. Lett. 27 (1971) 1668 [INSPIRE].
W. Israel and G.A. Wilson, A class of stationary electromagnetic vacuum fields, J. Math. Phys. 13 (1972) 865 [INSPIRE].
K.P. Tod, All Metrics Admitting Supercovariantly Constant Spinors, Phys. Lett. B 121 (1983) 241 [INSPIRE].
B. Whitt, Israel-Wilson Metrics, Annals Phys. 161 (1985) 241 [INSPIRE].
A.L. Yuille, Israel-Wilson Metrics in the Euclidean Regime, Class. Quant. Grav. 4 (1987) 1409 [INSPIRE].
Z.-W. Chong, M. Cvetic, H. Lu and C.N. Pope, General non-extremal rotating black holes in minimal five-dimensional gauged supergravity, Phys. Rev. Lett. 95 (2005) 161301 [hep-th/0506029] [INSPIRE].
B. de Wit and V. Reys, Euclidean supergravity, JHEP 12 (2017) 011 [arXiv:1706.04973] [INSPIRE].
V. Cortes and T. Mohaupt, Special Geometry of Euclidean Supersymmetry III: The local r-map, instantons and black holes, JHEP 07 (2009) 066 [arXiv:0905.2844] [INSPIRE].
M. Dunajski, J.B. Gutowski, W.A. Sabra and P. Tod, Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Beyond Self-Duality, JHEP 03 (2011) 131 [arXiv:1012.1326] [INSPIRE].
W.A. Sabra and O. Vaughan, Euclidean Supergravity in Five Dimensions, Phys. Lett. B 760 (2016) 14 [arXiv:1603.09244] [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge Univ. Press, Cambridge, U.K. (2012) [https://doi.org/10.1017/CBO9781139026833] [INSPIRE].
M. Dunajski and S.A. Hartnoll, Einstein-Maxwell gravitational instantons and five dimensional solitonic strings, Class. Quant. Grav. 24 (2007) 1841 [hep-th/0610261] [INSPIRE].
R. Emparan and H.S. Reall, Black Holes in Higher Dimensions, Living Rev. Rel. 11 (2008) 6 [arXiv:0801.3471] [INSPIRE].
K. Hristov, The dark (BPS) side of thermodynamics in Minkowski4, JHEP 09 (2022) 204 [arXiv:2207.12437] [INSPIRE].
I. Bena, S. Giusto, C. Ruef and N.P. Warner, Supergravity Solutions from Floating Branes, JHEP 03 (2010) 047 [arXiv:0910.1860] [INSPIRE].
A. Ciceri, I. Jeon and S. Murthy, Localization on AdS3 × S2. Part I. The 4d/5d connection in off-shell Euclidean supergravity, JHEP 07 (2023) 218 [arXiv:2301.08084] [INSPIRE].
M. Cvetic and D. Youm, General rotating five-dimensional black holes of toroidally compactified heterotic string, Nucl. Phys. B 476 (1996) 118 [hep-th/9603100] [INSPIRE].
M. Cvetic and F. Larsen, General rotating black holes in string theory: Grey body factors and event horizons, Phys. Rev. D 56 (1997) 4994 [hep-th/9705192] [INSPIRE].
J.P. Gauntlett et al., All supersymmetric solutions of minimal supergravity in five- dimensions, Class. Quant. Grav. 20 (2003) 4587 [hep-th/0209114] [INSPIRE].
I. Bena and N.P. Warner, Bubbling supertubes and foaming black holes, Phys. Rev. D 74 (2006) 066001 [hep-th/0505166] [INSPIRE].
I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [INSPIRE].
H. Elvang, R. Emparan, D. Mateos and H.S. Reall, A supersymmetric black ring, Phys. Rev. Lett. 93 (2004) 211302 [hep-th/0407065] [INSPIRE].
B. de Wit, J.W. van Holten and A. Van Proeyen, Structure of N = 2 Supergravity, Nucl. Phys. B 184 (1981) 77 [Erratum ibid. 222 (1983) 516] [INSPIRE].
B. de Wit, R. Philippe and A. Van Proeyen, The Improved Tensor Multiplet in N = 2 Supergravity, Nucl. Phys. B 219 (1983) 143 [INSPIRE].
Acknowledgments
We thank James Lucietti and Guillaume Bossard for email correspondence and Ashoke Sen for encouraging us to pursue this computation. It is a pleasure to also thank Chandramouli Chowdhury and P Shanmugapriya for interesting and useful discussions. We thank Guillaume Bossard for reading through an earlier version of the draft. We also thank an anonymous referee for insightful comments, which led to improvement in the presentation of the results.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2311.09427
Rights and permissions
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.
About this article
Cite this article
Hegde, S., Virmani, A. Killing spinors for finite temperature Euclidean solutions at the BPS bound. J. High Energ. Phys. 2024, 203 (2024). https://doi.org/10.1007/JHEP02(2024)203
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2024)203