Abstract
We reinterpret the OSV formula for the on-shell action/entropy function of asymptotically flat BPS black holes as a fixed point formula that is formally equivalent to a recent gluing proposal for asymptotically AdS4 black holes. This prompts a conjecture that the complete perturbative answer for the most general gravitational building block of 4d \( \mathcal{N} \) = 2 supergravity at a single fixed point takes the form of a Nekrasov-like partition function with equivariant parameters related to the higher-derivative expansion of the prepotential. In turn this leads to a simple localization-like proposal for a set of supersymmetric partition functions in (UV completed) 4d \( \mathcal{N} \) = 2 supergravity theories. The conjecture is shown to be in agreement with a number of available results for different BPS backgrounds with both Minkowski and AdS asymptotics. In particular, it follows that the OSV formula comes from the unrefined limit of the general expression including only the so-called 𝕎 tower of higher derivatives, while the on-shell action of pure (Euclidean) AdS4 with round S3 boundary comes from the NS limit that includes only the 𝕋 tower. Backgrounds preserving less supersymmetry, such as the under-rotating black holes in flat space, the holographic squashed S3, and the static/rotating twisted and non-twisted Kerr-Newman-like black holes in AdS4 lead to a more general refined version of the corresponding gravitational blocks as dictated by the supersymmetric gluing rules.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
H. Ooguri, A. Strominger and C. Vafa, Black hole attractors and the topological string, Phys. Rev. D 70 (2004) 106007 [hep-th/0405146] [INSPIRE].
F. Denef and G. W. Moore, Split states, entropy enigmas, holes and halos, JHEP 11 (2011) 129 [hep-th/0702146] [INSPIRE].
N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. 430 (1994) 485] [hep-th/9407087] [INSPIRE].
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [INSPIRE].
N. A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2003) 831 [hep-th/0206161] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
P. Benetti Genolini, J. M. Perez Ipiña and J. Sparks, Localization of the action in AdS/CFT, JHEP 10 (2019) 252 [arXiv:1906.11249] [INSPIRE].
S. M. Hosseini, K. Hristov and A. Zaffaroni, Gluing gravitational blocks for AdS black holes, JHEP 12 (2019) 168 [arXiv:1909.10550] [INSPIRE].
K. Hristov, S. Katmadas and I. Lodato, Higher derivative corrections to BPS black hole attractors in 4d gauged supergravity, JHEP 05 (2016) 173 [arXiv:1603.00039] [INSPIRE].
N. Bobev, A. M. Charles, K. Hristov and V. Reys, The unreasonable effectiveness of higher-derivative supergravity in AdS4 holography, Phys. Rev. Lett. 125 (2020) 131601 [arXiv:2006.09390] [INSPIRE].
N. Bobev, A. M. Charles, K. Hristov and V. Reys, Higher-derivative supergravity, AdS4 holography, and black holes, JHEP 08 (2021) 173 [arXiv:2106.04581] [INSPIRE].
K. Saraikin and C. Vafa, Non-supersymmetric black holes and topological strings, Class. Quant. Grav. 25 (2008) 095007 [hep-th/0703214] [INSPIRE].
N A. Nekrasov, Localizing gauge theories, in the proceedings of the 14th International Congress on Mathematical Physics, July 288–August 2, Lisbon, Portugal (2003).
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].
A. Dabholkar, N. Drukker and J. Gomes, Localization in supergravity and quantum AdS4/CFT3 holography, JHEP 10 (2014) 090 [arXiv:1406.0505] [INSPIRE].
K. Hristov, I. Lodato and V. Reys, On the quantum entropy function in 4d gauged supergravity, JHEP 07 (2018) 072 [arXiv:1803.05920] [INSPIRE].
B. de Wit, S. Murthy and V. Reys, BRST quantization and equivariant cohomology: localization with asymptotic boundaries, JHEP 09 (2018) 084 [arXiv:1806.03690] [INSPIRE].
L. Andrianopoli et al., N = 2 supergravity and N = 2 superYang-Mills theory on general scalar manifolds: Symplectic covariance, gaugings and the momentum map, J. Geom. Phys. 23 (1997) 111 [hep-th/9605032] [INSPIRE].
E. Lauria and A. Van Proeyen, \( \mathcal{N} \) = 2 supergravity in D = 4, 5, 6 dimensions, Springer, Germany (2020).
E. Bergshoeff, M. de Roo and B. de Wit, Extended conformal supergravity, Nucl. Phys. B 182 (1981) 173 [INSPIRE].
D. Butter, B. de Wit, S. M. Kuzenko and I. Lodato, New higher-derivative invariants in N = 2 supergravity and the Gauss-Bonnet term, JHEP 12 (2013) 062 [arXiv:1307.6546] [INSPIRE].
D. Butter, B. de Wit and I. Lodato, Non-renormalization theorems and N = 2 supersymmetric backgrounds, JHEP 03 (2014) 131 [arXiv:1401.6591] [INSPIRE].
N. Bobev, A. M. Charles, D. Gang, K. Hristov and V. Reys, Higher-derivative supergravity, wrapped M5-branes, and theories of class ℛ, JHEP 04 (2021) 058 [arXiv:2011.05971] [INSPIRE].
K. Hristov, S. Katmadas and C. Toldo, Rotating attractors and BPS black holes in AdS4, JHEP 01 (2019) 199 [arXiv:1811.00292] [INSPIRE].
C. Beem, T. Dimofte and S. Pasquetti, Holomorphic blocks in three dimensions, JHEP 12 (2014) 177 [arXiv:1211.1986] [INSPIRE].
J. F. Plebanski and M. Demianski, Rotating, charged, and uniformly accelerating mass in general relativity, Annals Phys. 98 (1976) 98 [INSPIRE].
D. Martelli, A. Passias and J. Sparks, The gravity dual of supersymmetric gauge theories on a squashed three-sphere, Nucl. Phys. B 864 (2012) 840 [arXiv:1110.6400] [INSPIRE].
D. Martelli and J. Sparks, The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere, Nucl. Phys. B 866 (2013) 72 [arXiv:1111.6930] [INSPIRE].
A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP 09 (2005) 038 [hep-th/0506177] [INSPIRE].
D. Z. Freedman and S. S. Pufu, The holography of F -maximization, JHEP 03 (2014) 135 [arXiv:1302.7310] [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].
D. Cassani and L. Papini, The BPS limit of rotating AdS black hole thermodynamics, JHEP 09 (2019) 079 [arXiv:1906.10148] [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].
F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS4 from supersymmetric localization, JHEP 05 (2016) 054 [arXiv:1511.04085] [INSPIRE].
F. Benini, K. Hristov and A. Zaffaroni, Exact microstate counting for dyonic black holes in AdS4, Phys. Lett. B 771 (2017) 462 [arXiv:1608.07294] [INSPIRE].
D. L. Jafferis, The exact superconformal R-symmetry extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].
D. L. Jafferis, I. R. Klebanov, S. S. Pufu and B. R. Safdi, Towards the F-theorem: N = 2 field theories on the three-sphere, JHEP 06 (2011) 102 [arXiv:1103.1181] [INSPIRE].
G. Bossard and S. Katmadas, Duality covariant non-BPS first order systems, JHEP 09 (2012) 100 [arXiv:1205.5461] [INSPIRE].
D. D. K. Chow and G. Compère, Black holes in N = 8 supergravity from SO(4, 4) hidden symmetries, Phys. Rev. D 90 (2014) 025029 [arXiv:1404.2602] [INSPIRE].
K. Hristov, S. Katmadas and V. Pozzoli, Ungauging black holes and hidden supercharges, JHEP 01 (2013) 110 [arXiv:1211.0035] [INSPIRE].
D. J. Binder, D. Z. Freedman, S. S. Pufu and B. Zan, The holographic contributions to the sphere free energy, JHEP 01 (2022) 171 [arXiv:2107.12382] [INSPIRE].
S. Choi and C. Hwang, Universal 3d Cardy block and black hole entropy, JHEP 03 (2020) 068 [arXiv:1911.01448] [INSPIRE].
A. Zaffaroni, AdS black holes, holography and localization, Living Rev. Rel. 23 (2020) 2 [arXiv:1902.07176] [INSPIRE].
K. Hristov, I. Lodato and V. Reys, One-loop determinants for black holes in 4d gauged supergravity, JHEP 11 (2019) 105 [arXiv:1908.05696] [INSPIRE].
K. Hristov and V. Reys, Factorization of log-corrections in AdS4/CFT3 from supergravity localization, JHEP 12 (2021) 031 [arXiv:2107.12398] [INSPIRE].
F. Azzurli, N. Bobev, P. M. Crichigno, V. S. Min and A. Zaffaroni, A universal counting of black hole microstates in AdS4, JHEP 02 (2018) 054 [arXiv:1707.04257] [INSPIRE].
N. Bobev and P. M. Crichigno, Universal RG flows across dimensions and holography, JHEP 12 (2017) 065 [arXiv:1708.05052] [INSPIRE].
P. B. Genolini and P. Richmond, Supersymmetry of higher-derivative supergravity in AdS4 holography, Phys. Rev. D 104 (2021) L061902 [arXiv:2107.04590] [INSPIRE].
S. Murthy and B. Pioline, A Farey tale for N = 4 dyons, JHEP 09 (2009) 022 [arXiv:0904.4253] [INSPIRE].
O. Aharony, F. Benini, O. Mamroud and P. Milan, A gravity interpretation for the Bethe Ansatz expansion of the \( \mathcal{N} \) = 4 SYM index, Phys. Rev. D 104 (2021) 086026 [arXiv:2104.13932] [INSPIRE].
J. Hong, The topologically twisted index of \( \mathcal{N} \) = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail, JHEP 10 (2021) 145 [arXiv:2108.02355] [INSPIRE].
A. Sen, Quantum entropy function from AdS2/CFT1 correspondence, Int. J. Mod. Phys. A 24 (2009) 4225 [arXiv:0809.3304] [INSPIRE].
O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
N. Drukker, M. Mariño and P. Putrov, Nonperturbative aspects of ABJM theory, JHEP 11 (2011) 141 [arXiv:1103.4844] [INSPIRE].
H. Fuji, S. Hirano and S. Moriyama, Summing up all genus free energy of ABJM matrix model, JHEP 08 (2011) 001 [arXiv:1106.4631] [INSPIRE].
M. Mariño and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 1203 (2012) P03001 [arXiv:1110.4066] [INSPIRE].
Y. Hatsuda, ABJM on ellipsoid and topological strings, JHEP 07 (2016) 026 [arXiv:1601.02728] [INSPIRE].
T. Nosaka, Instanton effects in ABJM theory with general R-charge assignments, JHEP 03 (2016) 059 [arXiv:1512.02862] [INSPIRE].
S. Murthy and V. Reys, Functional determinants, index theorems, and exact quantum black hole entropy, JHEP 12 (2015) 028 [arXiv:1504.01400] [INSPIRE].
V. Reys, Quantum black hole entropy and localization in supergravity, arXiv:1610.00466.
F. Benini and A. Zaffaroni, A topologically twisted index for three-dimensional supersymmetric theories, JHEP 07 (2015) 127 [arXiv:1504.03698] [INSPIRE].
F. Benini and A. Zaffaroni, Supersymmetric partition functions on Riemann surfaces, Proc. Symp. Pure Math. 96 (2017) 13 [arXiv:1605.06120] [INSPIRE].
S. Pasquetti, Factorisation of N = 2 theories on the squashed 3-sphere, JHEP 04 (2012) 120 [arXiv:1111.6905] [INSPIRE].
T. Dimofte, S. Gukov and L. Hollands, Vortex counting and Lagrangian 3-manifolds, Lett. Math. Phys. 98 (2011) 225 [arXiv:1006.0977] [INSPIRE].
C. Closset, H. Kim and B. Willett, Seifert fibering operators in 3d \( \mathcal{N} \) = 2 theories, JHEP 11 (2018) 004 [arXiv:1807.02328] [INSPIRE].
S. M. Hosseini and A. Zaffaroni, Large N matrix models for 3d \( \mathcal{N} \) = 2 theories: twisted index, free energy and black holes, JHEP 08 (2016) 064 [arXiv:1604.03122] [INSPIRE].
C. Closset, H. Kim and B. Willett, Supersymmetric partition functions and the three-dimensional A-twist, JHEP 03 (2017) 074 [arXiv:1701.03171] [INSPIRE].
Y. Hatsuda, M. Mariño, S. Moriyama and K. Okuyama, Non-perturbative effects and the refined topological string, JHEP 09 (2014) 168 [arXiv:1306.1734] [INSPIRE].
J. Kallen and M. Mariño, Instanton effects and quantum spectral curves, Annales Henri Poincaré 17 (2016) 1037 [arXiv:1308.6485] [INSPIRE].
K. Behrndt, D. Lüst and W. A. Sabra, Stationary solutions of N = 2 supergravity, Nucl. Phys. B 510 (1998) 264 [hep-th/9705169] [INSPIRE].
F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [INSPIRE].
G. Lopes Cardoso, B. de Wit and T. Mohaupt, Corrections to macroscopic supersymmetric black hole entropy, Phys. Lett. B 451 (1999) 309 [hep-th/9812082] [INSPIRE].
G. Lopes Cardoso, B. de Wit and T. Mohaupt, Deviations from the area law for supersymmetric black holes, Fortsch. Phys. 48 (2000) 49 [hep-th/9904005] [INSPIRE].
G. Lopes Cardoso, B. de Wit and T. Mohaupt, Macroscopic entropy formulae and nonholomorphic corrections for supersymmetric black holes, Nucl. Phys. B 567 (2000) 87 [hep-th/9906094] [INSPIRE].
G. Lopes Cardoso, B. de Wit, J. Kappeli and T. Mohaupt, Stationary BPS solutions in N = 2 supergravity with R2 interactions, JHEP 12 (2000) 019 [hep-th/0009234] [INSPIRE].
G. Lopes Cardoso, A. Ceresole, G. Dall’Agata, J. M. Oberreuter and J. Perz, First-order flow equations for extremal black holes in very special geometry, JHEP 10 (2007) 063 [arXiv:0706.3373] [INSPIRE].
E. G. Gimon, F. Larsen and J. Simon, Black holes in supergravity: the non-BPS branch, JHEP 01 (2008) 040 [arXiv:0710.4967] [INSPIRE].
I. Bena, G. Dall’Agata, S. Giusto, C. Ruef and N. P. Warner, Non-BPS black rings and black holes in Taub-NUT, JHEP 06 (2009) 015 [arXiv:0902.4526] [INSPIRE].
G. Dall’Agata, S. Giusto and C. Ruef, U-duality and non-BPS solutions, JHEP 02 (2011) 074 [arXiv:1012.4803] [INSPIRE].
B. Sahoo and A. Sen, Higher derivative corrections to non-supersymmetric extremal black holes in N = 2 supergravity, JHEP 09 (2006) 029 [hep-th/0603149] [INSPIRE].
N. Banerjee, S. Bansal and I. Lodato, The resolution of an entropy Puzzle for 4D non-BPS black holes, JHEP 05 (2016) 142 [arXiv:1602.05326] [INSPIRE].
S. L. Cacciatori and D. Klemm, Supersymmetric AdS4 black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926] [INSPIRE].
K. Hristov, S. Katmadas and C. Toldo, Matter-coupled supersymmetric Kerr-Newman-AdS4 black holes, Phys. Rev. D 100 (2019) 066016 [arXiv:1907.05192] [INSPIRE].
R. Emparan, C. V. Johnson and R. C. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238] [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].
C. Toldo and B. Willett, Partition functions on 3d circle bundles and their gravity duals, JHEP 05 (2018) 116 [arXiv:1712.08861] [INSPIRE].
P. Ferrero, J. P. Gauntlett, J. M. Pérez Ipiña, D. Martelli and J. Sparks, D3-branes wrapped on a Spindle, Phys. Rev. Lett. 126 (2021) 111601 [arXiv:2011.10579] [INSPIRE].
P. Ferrero, J. P. Gauntlett, J. M. P. Ipiña, D. Martelli and J. Sparks, Accelerating black holes and spinning spindles, Phys. Rev. D 104 (2021) 046007 [arXiv:2012.08530] [INSPIRE].
S. M. Hosseini, K. Hristov and A. Zaffaroni, Rotating multi-charge spindles and their microstates, JHEP 07 (2021) 182 [arXiv:2104.11249] [INSPIRE].
P. Ferrero, M. Inglese, D. Martelli and J. Sparks, Multi-charge accelerating black holes and spinning spindles, arXiv:2109.14625 [INSPIRE].
N. Bobev, P. Bomans and F. F. Gautason, Wrapped branes and punctured horizons, JHEP 06 (2020) 011 [arXiv:1912.04779] [INSPIRE].
R. Monten and C. Toldo, On the search for multicenter AdS black holes from M-theory, JHEP 02 (2022) 009 [arXiv:2111.06879] [INSPIRE].
K. Hristov, H. Looyestijn and S. Vandoren, BPS black holes in N = 2 D = 4 gauged supergravities, JHEP 08 (2010) 103 [arXiv:1005.3650] [INSPIRE].
S. M. Hosseini, K. Hristov and A. Passias, Holographic microstate counting for AdS4 black holes in massive IIA supergravity, JHEP 10 (2017) 190 [arXiv:1707.06884] [INSPIRE].
S. M. Hosseini, K. Hristov, Y. Tachikawa and A. Zaffaroni, Anomalies, Black strings and the charged Cardy formula, JHEP 09 (2020) 167 [arXiv:2006.08629] [INSPIRE].
N. Banerjee, B. de Wit and S. Katmadas, The off-shell 4D/5D connection, JHEP 03 (2012) 061 [arXiv:1112.5371] [INSPIRE].
S. M. Hosseini, I. Yaakov and A. Zaffaroni, Topologically twisted indices in five dimensions and holography, JHEP 11 (2018) 119 [arXiv:1808.06626] [INSPIRE].
S. M. Hosseini, I. Yaakov and A. Zaffaroni, The joy of factorization at large N: five-dimensional indices and AdS black holes, arXiv:2111.03069 [INSPIRE].
T. Mohaupt, Black hole entropy, special geometry and strings, Fortsch. Phys. 49 (2001) 3 [hep-th/0007195] [INSPIRE].
B. de Wit and V. Reys, Euclidean supergravity, JHEP 12 (2017) 011 [arXiv:1706.04973] [INSPIRE].
B. de Wit, S. Katmadas and M. van Zalk, New supersymmetric higher-derivative couplings: full N = 2 superspace does not count!, JHEP 01 (2011) 007 [arXiv:1010.2150] [INSPIRE].
K. Behrndt, G. Lopes Cardoso, B. de Wit, R. Kallosh, D. Lüst and T. Mohaupt, Classical and quantum N = 2 supersymmetric black holes, Nucl. Phys. B 488 (1997) 236 [hep-th/9610105] [INSPIRE].
B. de Wit and F. Saueressig, Off-shell N = 2 tensor supermultiplets, JHEP 09 (2006) 062 [hep-th/0606148] [INSPIRE].
S. M. Kuzenko and J. Novak, On curvature squared terms in N = 2 supergravity, Phys. Rev. D 92 (2015) 085033 [arXiv:1507.04922] [INSPIRE].
S. Hegde and B. Sahoo, New higher derivative action for tensor multiplet in \( \mathcal{N} \) = 2 conformal supergravity in four dimensions, JHEP 01 (2020) 070 [arXiv:1911.09585] [INSPIRE].
S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) R5412 [hep-th/9508072] [INSPIRE].
S. Ferrara and R. Kallosh, Supersymmetry and attractors, Phys. Rev. D 54 (1996) 1514 [hep-th/9602136] [INSPIRE].
S. Ferrara and R. Kallosh, Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525 [hep-th/9603090] [INSPIRE].
H. Lü, C. N. Pope and J. Rahmfeld, A construction of Killing spinors on Sn, J. Math. Phys. 40 (1999) 4518 [hep-th/9805151] [INSPIRE].
K. Hristov, Lessons from the vacuum structure of 4d N = 2 supergravity, arXiv:1207.3830.
J. M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP 12 (1997) 002 [hep-th/9711053] [INSPIRE].
S. Murthy and V. Reys, Quantum black hole entropy and the holomorphic prepotential of N = 2 supergravity, JHEP 10 (2013) 099 [arXiv:1306.3796] [INSPIRE].
B. de Wit and M. van Zalk, Electric and magnetic charges in N = 2 conformal supergravity theories, JHEP 10 (2011) 050 [arXiv:1107.3305] [INSPIRE].
M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Holomorphic anomalies in topological field theories, Nucl. Phys. B 405 (1993) 279 [hep-th/9302103] [INSPIRE].
M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes, Commun. Math. Phys. 165 (1994) 311 [hep-th/9309140] [INSPIRE].
I. Antoniadis, E. Gava, K. S. Narain and T. R. Taylor, Topological amplitudes in string theory, Nucl. Phys. B 413 (1994) 162 [hep-th/9307158] [INSPIRE].
S. Murthy and V. Reys, Single-centered black hole microstate degeneracies from instantons in supergravity, JHEP 04 (2016) 052 [arXiv:1512.01553] [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].
A. Gnecchi, K. Hristov, D. Klemm, C. Toldo and O. Vaughan, Rotating black holes in 4d gauged supergravity, JHEP 01 (2014) 127 [arXiv:1311.1795] [INSPIRE].
K. Hristov and A. Rota, 6d-5d-4d reduction of BPS attractors in flat gauged supergravities, Nucl. Phys. B 897 (2015) 213 [arXiv:1410.5386] [INSPIRE].
K. Hanaki, K. Ohashi and Y. Tachikawa, Supersymmetric completion of an R2 term in Five-dimensional supergravity, Prog. Theor. Phys. 117 (2007) 533 [hep-th/0611329] [INSPIRE].
M. Aganagic, M. C. N. Cheng, R. Dijkgraaf, D. Krefl and C. Vafa, Quantum Geometry of Refined Topological Strings, JHEP 11 (2012) 019 [arXiv:1105.0630] [INSPIRE].
M. Aganagic and K. Schaeffer, Refined black hole ensembles and topological strings, JHEP 01 (2013) 060 [arXiv:1210.1865] [INSPIRE].
S. Alexandrov, J. Manschot and B. Pioline, S-duality and refined BPS indices, Commun. Math. Phys. 380 (2020) 755 [arXiv:1910.03098] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact results for Wilson loops in superconformal Chern-Simons theories with matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, SUSY gauge theories on squashed three-spheres, JHEP 05 (2011) 014 [arXiv:1102.4716] [INSPIRE].
K. Hristov, H. Looyestijn and S. Vandoren, Maximally supersymmetric solutions of D = 4 N = 2 gauged supergravity, JHEP 11 (2009) 115 [arXiv:0909.1743] [INSPIRE].
I. R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
M. Bianchi, D. Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
S. M. Hosseini, C. Toldo and I. Yaakov, Supersymmetric Rényi entropy and charged hyperbolic black holes, JHEP 07 (2020) 131 [arXiv:1912.04868] [INSPIRE].
A. Grassi, Y. Hatsuda and M. Mariño, Topological strings from quantum mechanics, Annales Henri Poincaré 17 (2016) 3177 [arXiv:1410.3382] [INSPIRE].
S. M. Chester, R. R. Kalloor and A. Sharon, Squashing, mass, and holography for 3d sphere free energy, JHEP 04 (2021) 244 [arXiv:2102.05643] [INSPIRE].
M. Mezei and S. S. Pufu, Three-sphere free energy for classical gauge groups, JHEP 02 (2014) 037 [arXiv:1312.0920] [INSPIRE].
M. Fluder and J. Sparks, D2-brane Chern-Simons theories: F-maximization = a-maximization, JHEP 01 (2016) 048 [arXiv:1507.05817] [INSPIRE].
S. M. Hosseini and N. Mekareeya, Large N topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces, JHEP 08 (2016) 089 [arXiv:1604.03397] [INSPIRE].
S. Katmadas, Static BPS black holes in U(1) gauged supergravity, JHEP 09 (2014) 027 [arXiv:1405.4901] [INSPIRE].
N. Halmagyi, Static BPS black holes in AdS4 with general dyonic charges, JHEP 03 (2015) 032 [arXiv:1408.2831] [INSPIRE].
K. Hristov, C. Toldo and S. Vandoren, On BPS bounds in D = 4 N = 2 gauged supergravity, JHEP 12 (2011) 014 [arXiv:1110.2688] [INSPIRE].
K. Hristov, On BPS Bounds in D = 4 N = 2 Gauged Supergravity. Part II. General matter couplings and black hole masses, JHEP 03 (2012) 095 [arXiv:1112.4289] [INSPIRE].
K. Hristov, A. Tomasiello and A. Zaffaroni, Supersymmetry on three-dimensional Lorentzian curved spaces and black hole holography, JHEP 05 (2013) 057 [arXiv:1302.5228] [INSPIRE].
M. M. Caldarelli and D. Klemm, Supersymmetry of Anti-de Sitter black holes, Nucl. Phys. B 545 (1999) 434 [hep-th/9808097] [INSPIRE].
S. L. Cacciatori, D. Klemm, D. S. Mansi and E. Zorzan, All timelike supersymmetric solutions of N = 2, D = 4 gauged supergravity coupled to abelian vector multiplets, JHEP 05 (2008) 097 [arXiv:0804.0009] [INSPIRE].
P. Meessen and T. Ortín, Supersymmetric solutions to gauged N = 2 d = 4 SUGRA: the full timelike shebang, Nucl. Phys. B 863 (2012) 65 [arXiv:1204.0493] [INSPIRE].
G. Dall’Agata and A. Gnecchi, Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity, JHEP 03 (2011) 037 [arXiv:1012.3756] [INSPIRE].
K. Hristov and S. Vandoren, Static supersymmetric black holes in AdS4 with spherical symmetry, JHEP 04 (2011) 047 [arXiv:1012.4314] [INSPIRE].
A. Guarino, BPS black hole horizons from massive IIA, JHEP 08 (2017) 100 [arXiv:1706.01823] [INSPIRE].
F. Benini, H. Khachatryan and P. Milan, Black hole entropy in massive Type IIA, Class. Quant. Grav. 35 (2018) 035004 [arXiv:1707.06886] [INSPIRE].
N. Bobev, V. S. Min and K. Pilch, Mass-deformed ABJM and black holes in AdS4, JHEP 03 (2018) 050 [arXiv:1801.03135] [INSPIRE].
D. Gang, N. Kim and L. A. Pando Zayas, Precision microstate counting for the entropy of wrapped M5-branes, JHEP 03 (2020) 164 [arXiv:1905.01559] [INSPIRE].
F. Benini, D. Gang and L. A. Pando Zayas, Rotating black hole entropy from M5 branes, JHEP 03 (2020) 057 [arXiv:1909.11612] [INSPIRE].
L. Coccia, Topologically twisted index of T [SU(N)] at large N, JHEP 05 (2021) 264 [arXiv:2006.06578] [INSPIRE].
S. M. Hosseini and A. Zaffaroni, Universal AdS black holes in theories with 16 supercharges and their microstates, Phys. Rev. Lett. 126 (2021) 171604 [arXiv:2011.01249] [INSPIRE].
S. M. Hosseini and K. Hristov, 4d F (4) gauged supergravity and black holes of class ℱ, JHEP 02 (2021) 177 [arXiv:2011.01943] [INSPIRE].
J. T. Liu, L. A. Pando Zayas, V. Rathee and W. Zhao, Toward microstate counting beyond large N in localization and the dual one-loop quantum supergravity, JHEP 01 (2018) 026 [arXiv:1707.04197] [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].
J. T. Liu, L. A. Pando Zayas, V. Rathee and W. Zhao, One-loop test of quantum black holes in Anti-de Sitter space, Phys. Rev. Lett. 120 (2018) 221602 [arXiv:1711.01076] [INSPIRE].
J. T. Liu, L. A. Pando Zayas and S. Zhou, Subleading microstate counting in the dual to massive type IIA, arXiv:1808.10445 [INSPIRE].
L. A. Pando Zayas and Y. Xin, Topologically twisted index in the ’t Hooft limit and the dual AdS4 black hole entropy, Phys. Rev. D 100 (2019) 126019 [arXiv:1908.01194] [INSPIRE].
V. A. Kostelecky and M. J. Perry, Solitonic black holes in gauged N = 2 supergravity, Phys. Lett. B 371 (1996) 191 [hep-th/9512222] [INSPIRE].
M. Cvetič, G. W. Gibbons, H. Lü and C. N. Pope, Rotating black holes in gauged supergravities: thermodynamics, supersymmetric limits, topological solitons and time machines, hep-th/0504080 [INSPIRE].
D. D. K. Chow and G. Compère, Dyonic AdS black holes in maximal gauged supergravity, Phys. Rev. D 89 (2014) 065003 [arXiv:1311.1204] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and S. Raju, Indices for superconformal field theories in 3, 5 and 6 dimensions, JHEP 02 (2008) 064 [arXiv:0801.1435] [INSPIRE].
S. Kim, The Complete superconformal index for N = 6 Chern-Simons theory, Nucl. Phys. B 821 (2009) 241 [Erratum ibid. 864 (2012) 884] [arXiv:0903.4172] [INSPIRE].
Y. Imamura and S. Yokoyama, Index for three dimensional superconformal field theories with general R-charge assignments, JHEP 04 (2011) 007 [arXiv:1101.0557] [INSPIRE].
A. Kapustin and B. Willett, Generalized superconformal index for three dimensional field theories, arXiv:1106.2484 [INSPIRE].
S. Choi, C. Hwang, S. Kim and J. Nahmgoong, Entropy functions of BPS black holes in AdS4 and AdS6, J. Korean Phys. Soc. 76 (2020) 101 [arXiv:1811.02158] [INSPIRE].
S. Choi, C. Hwang and S. Kim, Quantum vortices, M2-branes and black holes, arXiv:1908.02470 [INSPIRE].
N. Bobev and P. M. Crichigno, Universal spinning black holes and theories of class ℛ, JHEP 12 (2019) 054 [arXiv:1909.05873] [INSPIRE].
J. Nian and L.A. Pando Zayas, Microscopic entropy of rotating electrically charged AdS4 black holes from field theory localization, JHEP 03 (2020) 081 [arXiv:1909.07943] [INSPIRE].
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: 2111.06903
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
Hristov, K. 4d \( \mathcal{N} \) = 2 supergravity observables from Nekrasov-like partition functions. J. High Energ. Phys. 2022, 79 (2022). https://doi.org/10.1007/JHEP02(2022)079
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2022)079