Abstract
We provide a unifying entropy functional and an extremization principle for black holes and black strings in AdS4 × S7 and AdS5 × S5 with arbitrary rotation and generic electric and magnetic charges. This is done by gluing gravitational blocks, basic building blocks that are directly inspired by the holomorphic blocks appearing in the factorization of supersymmetric partition functions in three and four dimensions. We also provide an explicit realization of the attractor mechanism by identifying the values of the scalar fields at the horizon with the critical points of the entropy functional. We give examples based on dyonic rotating black holes with a twist in AdS4 × S7, rotating black strings in AdS5 × S5, dyonic Kerr-Newman black holes in AdS4 × S7 and Kerr-Newman black holes in AdS5 × S5. In particular, our entropy functional extends existing results by adding rotation to the twisted black holes in AdS4 and by adding flavor magnetic charges for the Kerr-Newman black holes in AdS4. We also discuss generalizations to higher-dimensional black objects.
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F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS 4from supersymmetric localization, JHEP05 (2016) 054 [arXiv:1511.04085] [INSPIRE].
A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS 5black holes, JHEP10 (2019) 062 [arXiv:1810.11442] [INSPIRE].
S. Choi, J. Kim, S. Kim and J. Nahmgoong, Large AdS black holes from QFT, arXiv:1810.12067 [INSPIRE].
F. Benini and P. Milan, Black holes in 4d \( \mathcal{N} \) = 4 Super-Yang-Mills, arXiv:1812.09613 [INSPIRE].
S. Ferrara and R. Kallosh, Supersymmetry and attractors, Phys. Rev.D 54 (1996) 1514 [hep-th/9602136] [INSPIRE].
S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev.D 52 (1995) R5412 [hep-th/9508072] [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].
A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP09 (2005) 038 [hep-th/0506177] [INSPIRE].
S.L. Cacciatori and D. Klemm, Supersymmetric AdS 4black holes and attractors, JHEP01 (2010) 085 [arXiv:0911.4926] [INSPIRE].
G. Dall’Agata and A. Gnecchi, Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity, JHEP03 (2011) 037 [arXiv:1012.3756] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, An extremization principle for the entropy of rotating BPS black holes in AdS 5, JHEP07 (2017) 106 [arXiv:1705.05383] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, A note on the entropy of rotating BPS AdS 7 × S 4black holes, JHEP05 (2018) 121 [arXiv:1803.07568] [INSPIRE].
S. Choi, C. Hwang, S. Kim and J. Nahmgoong, Entropy functions of BPS black holes in AdS 4and AdS 6, arXiv:1811.02158 [INSPIRE].
D. Cassani and L. Papini, The BPS limit of rotating AdS black hole thermodynamics, JHEP09 (2019) 079 [arXiv:1906.10148] [INSPIRE].
S. Katmadas, Static BPS black holes in U(1) gauged supergravity, JHEP09 (2014) 027 [arXiv:1405.4901] [INSPIRE].
N. Halmagyi, Static BPS black holes in AdS 4with general dyonic charges, JHEP03 (2015) 032 [arXiv:1408.2831] [INSPIRE].
K. Hristov, S. Katmadas and C. Toldo, Rotating attractors and BPS black holes in AdS 4, JHEP01 (2019) 199 [arXiv:1811.00292] [INSPIRE].
F. Benini and N. Bobev, Two-dimensional SCFTs from wrapped branes and c-extremization, JHEP06 (2013) 005 [arXiv:1302.4451] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, Microstates of rotating AdS 5strings, JHEP11 (2019) 090 [arXiv:1909.08000] [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].
K. Hristov, S. Katmadas and C. Toldo, Matter-coupled supersymmetric Kerr-Newman-AdS 4black holes, Phys. Rev.D 100 (2019) 066016 [arXiv:1907.05192] [INSPIRE].
J.B. Gutowski and H.S. Reall, Supersymmetric AdS 5black holes, JHEP02 (2004) 006 [hep-th/0401042] [INSPIRE].
H.K. Kunduri, J. Lucietti and H.S. Reall, Supersymmetric multi-charge AdS 5black holes, JHEP04 (2006) 036 [hep-th/0601156] [INSPIRE].
D. Astefanesei, K. Goldstein, R.P. Jena, A. Sen and S.P. Trivedi, Rotating attractors, JHEP10 (2006) 058 [hep-th/0606244] [INSPIRE].
C. Beem, T. Dimofte and S. Pasquetti, Holomorphic Blocks in Three Dimensions, JHEP12 (2014) 177 [arXiv:1211.1986] [INSPIRE].
A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory, Nucl. Phys.B 241 (1984) 333 [INSPIRE].
N.A. Nekrasov, Localizing gauge theories, in Mathematical physics. Proceedings of 14th International Congress, ICMP 2003, Lisbon Portugal (2003), pg. 645.
S. Pasquetti, Factorisation of N = 2 Theories on the Squashed 3-Sphere, JHEP04 (2012) 120 [arXiv:1111.6905] [INSPIRE].
C. Hwang, H.-C. Kim and J. Park, Factorization of the 3d superconformal index, JHEP08 (2014) 018 [arXiv:1211.6023] [INSPIRE].
Y. Imamura, H. Matsuno and D. Yokoyama, Factorization of the S 3/ℤnpartition function, Phys. Rev.D 89 (2014) 085003 [arXiv:1311.2371] [INSPIRE].
Y. Yoshida and K. Sugiyama, Localization of 3d \( \mathcal{N} \) = 2 Supersymmetric Theories on S 1 × D 2, arXiv:1409.6713 [INSPIRE].
C. Hwang and J. Park, Factorization of the 3d superconformal index with an adjoint matter, JHEP11 (2015) 028 [arXiv:1506.03951] [INSPIRE].
F. Benini and A. Zaffaroni, A topologically twisted index for three-dimensional supersymmetric theories, JHEP07 (2015) 127 [arXiv:1504.03698] [INSPIRE].
F. Nieri and S. Pasquetti, Factorisation and holomorphic blocks in 4d, JHEP11 (2015) 155 [arXiv:1507.00261] [INSPIRE].
S. Gukov, D. Pei, P. Putrov and C. Vafa, BPS spectra and 3-manifold invariants, arXiv:1701.06567 [INSPIRE].
C. Closset, H. Kim and B. Willett, Seifert fibering operators in 3d \( \mathcal{N} \) = 2 theories, JHEP11 (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, JHEP08 (2016) 064 [arXiv:1604.03122] [INSPIRE].
S.M. Hosseini, A. Nedelin and A. Zaffaroni, The Cardy limit of the topologically twisted index and black strings in AdS 5, JHEP04 (2017) 014 [arXiv:1611.09374] [INSPIRE].
S.M. Hosseini and N. Mekareeya, Large N topologically twisted index: necklace quivers, dualities and Sasaki-Einstein spaces, JHEP08 (2016) 089 [arXiv:1604.03397] [INSPIRE].
D. Jain and A. Ray, 3d \( \mathcal{N} \) = 2 \( \hat{ADE} \)Chern-Simons quivers, Phys. Rev.D 100 (2019) 046007 [arXiv:1902.10498] [INSPIRE].
D. Jain, Twisted Indices of more 3d Quivers, arXiv:1908.03035 [INSPIRE].
F. Benini, K. Hristov and A. Zaffaroni, Exact microstate counting for dyonic black holes in AdS 4, Phys. Lett.B 771 (2017) 462 [arXiv:1608.07294] [INSPIRE].
S. Choi, C. Hwang and S. Kim, Quantum vortices, M2-branes and black holes, arXiv:1908.02470 [INSPIRE].
J. Nian and L.A. Pando Zayas, Microscopic Entropy of Rotating Electrically Charged AdS 4Black Holes from Field Theory Localization, arXiv:1909.07943 [INSPIRE].
D.D.K. Chow, Charged rotating black holes in six-dimensional gauged supergravity, Class. Quant. Grav.27 (2010) 065004 [arXiv:0808.2728] [INSPIRE].
D.D.K. Chow, Equal charge black holes and seven dimensional gauged supergravity, Class. Quant. Grav.25 (2008) 175010 [arXiv:0711.1975] [INSPIRE].
S.M. Hosseini, K. Hristov, A. Passias and A. Zaffaroni, 6D attractors and black hole microstates, arXiv:1809.10685 [INSPIRE].
A. Brandhuber and Y. Oz, The D-4–D-8 brane system and five-dimensional fixed points, Phys. Lett.B 460 (1999) 307 [hep-th/9905148] [INSPIRE].
K. Hristov, C. Toldo and S. Vandoren, On BPS bounds in D = 4 N = 2 gauged supergravity, JHEP12 (2011) 014 [arXiv:1110.2688] [INSPIRE].
K. Hristov, A. Tomasiello and A. Zaffaroni, Supersymmetry on Three-dimensional Lorentzian Curved Spaces and Black Hole Holography, JHEP05 (2013) 057 [arXiv:1302.5228] [INSPIRE].
M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys.B 558 (1999) 96 [hep-th/9903214] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
F. Benini and N. Bobev, Exact two-dimensional superconformal R-symmetry and c-extremization, Phys. Rev. Lett.110 (2013) 061601 [arXiv:1211.4030] [INSPIRE].
D. Gaiotto, A. Strominger and X. Yin, New connections between 4 − D and 5 − D black holes, JHEP02 (2006) 024 [hep-th/0503217] [INSPIRE].
K. Behrndt, G. Lopes Cardoso and S. Mahapatra, Exploring the relation between 4 − D and 5 − D BPS solutions, Nucl. Phys.B 732 (2006) 200 [hep-th/0506251] [INSPIRE].
K. Hristov, Dimensional reduction of BPS attractors in AdS gauged supergravities, JHEP12 (2014) 066 [arXiv:1409.8504] [INSPIRE].
K. Hristov and S. Katmadas, Wilson lines for AdS 5black strings, JHEP02 (2015) 009 [arXiv:1411.2432] [INSPIRE].
A. Kapustin and B. Willett, Generalized Superconformal Index for Three Dimensional Field Theories, arXiv:1106.2484 [INSPIRE].
Z.W. Chong, M. Cvetič, H. Lü 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].
H.K. Kunduri and J. Lucietti, Near-horizon geometries of supersymmetric AdS 5black holes, JHEP12 (2007) 015 [arXiv:0708.3695] [INSPIRE].
J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An Index for 4 dimensional super conformal theories, Commun. Math. Phys.275 (2007) 209 [hep-th/0510251] [INSPIRE].
C. Romelsberger, Counting chiral primaries in N = 1, d = 4 superconformal field theories, Nucl. Phys.B 747 (2006) 329 [hep-th/0510060] [INSPIRE].
M. Honda, Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula, Phys. Rev. D 100 (2019) 026008 [arXiv:1901.08091] [INSPIRE].
A. Arabi Ardehali, Cardy-like asymptotics of the 4d \( \mathcal{N} \) = 4 index and AdS 5blackholes, JHEP06 (2019) 134 [arXiv:1902.06619] [INSPIRE].
J. Kim, S. Kim and J. Song, A 4d N = 1 Cardy Formula, arXiv:1904.03455 [INSPIRE].
A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, The asymptotic growth of states of the 4d \( \mathcal{N} \) = 1 superconformal index, JHEP08 (2019) 120 [arXiv:1904.05865] [INSPIRE].
A. Amariti, I. Garozzo and G. Lo Monaco, Entropy function from toric geometry, arXiv:1904.10009 [INSPIRE].
F. Larsen, J. Nian and Y. Zeng, AdS 5Black Hole Entropy near the BPS Limit, arXiv:1907.02505 [INSPIRE].
A.G. Lezcano and L.A. Pando Zayas, Microstate Counting via Bethe Ansätze in the 4d \( \mathcal{N} \) = 1 Superconformal Index, arXiv:1907.12841 [INSPIRE].
A. Lanir, A. Nedelin and O. Sela, Black hole entropy function for toric theories via Bethe Ansatz, arXiv:1908.01737 [INSPIRE].
L. Andrianopoli, S. Ferrara and M.A. Lledó, Scherk-Schwarz reduction of D = 5 special and quaternionic geometry, Class. Quant. Grav.21 (2004) 4677 [hep-th/0405164] [INSPIRE].
H. Looyestijn, E. Plauschinn and S. Vandoren, New potentials from Scherk-Schwarz reductions, JHEP12 (2010) 016 [arXiv:1008.4286] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, work in progress.
Y. Yoshida, Factorization of 4d N = 1 superconformal index, arXiv:1403.0891 [INSPIRE].
W. Peelaers, Higgs branch localization of \( \mathcal{N} \) = 1 theories on S 3 × S 1, JHEP08 (2014) 060 [arXiv:1403.2711] [INSPIRE].
M. Suh, Supersymmetric AdS 6black holes from matter coupled F (4) gauged supergravity, JHEP02 (2019) 108 [arXiv:1810.00675] [INSPIRE].
S.M. Hosseini, I. Yaakov and A. Zaffaroni, Topologically twisted indices in five dimensions and holography, JHEP11 (2018) 119 [arXiv:1808.06626] [INSPIRE].
P.M. Crichigno, D. Jain and B. Willett, 5d Partition Functions with A Twist, JHEP11 (2018) 058 [arXiv:1808.06744] [INSPIRE].
A. Bawane, G. Bonelli, M. Ronzani and A. Tanzini, \( \mathcal{N} \) = 2 supersymmetric gauge theories on S 2 × S 2and Liouville Gravity, JHEP07 (2015) 054 [arXiv:1411.2762] [INSPIRE].
M. Bershtein, G. Bonelli, M. Ronzani and A. Tanzini, Exact results for \( \mathcal{N} \) = 2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants, JHEP07 (2016) 023 [arXiv:1509.00267] [INSPIRE].
N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett.B 388 (1996) 753 [hep-th/9608111] [INSPIRE].
D.L. Jafferis and S.S. Pufu, Exact results for five-dimensional superconformal field theories with gravity duals, JHEP05 (2014) 032 [arXiv:1207.4359] [INSPIRE].
R. D’Auria, S. Ferrara and S. Vaula, F (4) supergravity and 5 − D superconformal field theories, Class. Quant. Grav.18 (2001) 3181 [hep-th/0008209] [INSPIRE].
L. Andrianopoli, R. D’Auria and S. Vaula, Matter coupled F (4) gauged supergravity Lagrangian, JHEP05 (2001) 065 [hep-th/0104155] [INSPIRE].
P. Benetti Genolini, J.M. Perez Ipiña and J. Sparks, Localization of the action in AdS/CFT, JHEP10 (2019) 252 [arXiv:1906.11249] [INSPIRE].
K. Hristov, I. Lodato and V. Reys, One-loop determinants for black holes in 4d gauged supergravity, JHEP11 (2019) 105 [arXiv:1908.05696] [INSPIRE].
K. Hristov, I. Lodato and V. Reys, On the quantum entropy function in 4d gauged supergravity, JHEP07 (2018) 072 [arXiv:1803.05920] [INSPIRE].
A. Guarino and J. Tarrío, BPS black holes from massive IIA on S 6, JHEP09 (2017) 141 [arXiv:1703.10833] [INSPIRE].
A. Guarino, BPS black hole horizons from massive IIA, JHEP08 (2017) 100 [arXiv:1706.01823] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Passias, Holographic microstate counting for AdS 4black holes in massive IIA supergravity, JHEP10 (2017) 190 [arXiv:1707.06884] [INSPIRE].
F. Azzurli, N. Bobev, P.M. Crichigno, V.S. Min and A. Zaffaroni, A universal counting of black hole microstates in AdS 4, JHEP02 (2018) 054 [arXiv:1707.04257] [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].
A. Guarino, D.L. Jafferis and O. Varela, String Theory Origin of Dyonic N = 8 Supergravity and Its Chern-Simons Duals, Phys. Rev. Lett.115 (2015) 091601 [arXiv:1504.08009] [INSPIRE].
M.M. Caldarelli and D. Klemm, Supersymmetry of Anti-de Sitter black holes, Nucl. Phys. B 545 (1999) 434 [hep-th/9808097] [INSPIRE].
A. Ceresole and G. Dall’Agata, Flow Equations for Non-BPS Extremal Black Holes, JHEP03 (2007) 110 [hep-th/0702088] [INSPIRE].
D. Klemm and O. Vaughan, Nonextremal black holes in gauged supergravity and the real formulation of special geometry II, Class. Quant. Grav.30 (2013) 065003 [arXiv:1211.1618] [INSPIRE].
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].
L. Andrianopoli et al., N = 2 supergravity and N = 2 super Yang-Mills theory on general scalar manifolds: Symplectic covariance, gaugings and the momentum map, J. Geom. Phys.23 (1997) 111 [hep-th/9605032] [INSPIRE].
A. Gnecchi and N. Halmagyi, Supersymmetric black holes in AdS 4from very special geometry, JHEP04 (2014) 173 [arXiv:1312.2766] [INSPIRE].
S. Ferrara and M. Günaydin, Orbits of exceptional groups, duality and BPS states in string theory, Int. J. Mod. Phys.A 13 (1998) 2075 [hep-th/9708025] [INSPIRE].
S. Ferrara, E.G. Gimon and R. Kallosh, Magic supergravities, N = 8 and black hole composites, Phys. Rev.D 74 (2006) 125018 [hep-th/0606211] [INSPIRE].
G. Bossard and S. Katmadas, Duality covariant multi-centre black hole systems, JHEP08 (2013) 007 [arXiv:1304.6582] [INSPIRE].
G. Bossard and S. Katmadas, Duality covariant non-BPS first order systems, JHEP09 (2012) 100 [arXiv:1205.5461] [INSPIRE].
K. Hristov, S. Katmadas and V. Pozzoli, Ungauging black holes and hidden supercharges, JHEP01 (2013) 110 [arXiv:1211.0035] [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].
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Hosseini, S.M., Hristov, K. & Zaffaroni, A. Gluing gravitational blocks for AdS black holes. J. High Energ. Phys. 2019, 168 (2019). https://doi.org/10.1007/JHEP12(2019)168
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DOI: https://doi.org/10.1007/JHEP12(2019)168