Abstract
We study the flow equations for BPS black holes in \( \mathcal{N} \) = 2 five-dimensional gauged supergravity coupled to any number of vector multiplets via FI couplings. We develop the Noether-Wald procedure in this context and exhibit the conserved charges as explicit integrals of motion, in the sense that they can be computed at any radius on the rotating spacetime. The boundary conditions needed to solve the first order differential equations are discussed in great detail. We extremize the entropy function that controls the near horizon geometry and give explicit formulae for all geometric variables at their supersymmetric extrema. We have also considered a complexification of the near-horizon variables that elucidates some features of the theory from the near-horizon perspective.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP 09 (2005) 038 [hep-th/0506177] [INSPIRE].
A. Sen, Entropy function for heterotic black holes, JHEP 03 (2006) 008 [hep-th/0508042] [INSPIRE].
J.R. David and A. Sen, CHL Dyons and Statistical Entropy Function from D1-D5 System, JHEP 11 (2006) 072 [hep-th/0605210] [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, Entropy Function and AdS(2) / CFT(1) Correspondence, JHEP 11 (2008) 075 [arXiv:0805.0095] [INSPIRE].
A. Sen, Quantum Entropy Function from AdS(2)/CFT(1) 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].
D. Astefanesei et al., Rotating attractors, JHEP 10 (2006) 058 [hep-th/0606244] [INSPIRE].
A. Castro, J.L. Davis, P. Kraus and F. Larsen, 5D attractors with higher derivatives, JHEP 04 (2007) 091 [hep-th/0702072] [INSPIRE].
P. Kraus and F. Larsen, Microscopic black hole entropy in theories with higher derivatives, JHEP 09 (2005) 034 [hep-th/0506176] [INSPIRE].
N. Banerjee et al., Supersymmetry, Localization and Quantum Entropy Function, JHEP 02 (2010) 091 [arXiv:0905.2686] [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. 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].
S. Ferrara and R. Kallosh, On N=8 attractors, Phys. Rev. D 73 (2006) 125005 [hep-th/0603247] [INSPIRE].
F. Larsen, The Attractor Mechanism in Five Dimensions, Lect. Notes Phys. 755 (2008) 249 [hep-th/0608191] [INSPIRE].
A. Ceresole and G. Dall’Agata, Flow Equations for Non-BPS Extremal Black Holes, JHEP 03 (2007) 110 [hep-th/0702088] [INSPIRE].
G. Lopes Cardoso et al., First-order flow equations for extremal black holes in very special geometry, JHEP 10 (2007) 063 [arXiv:0706.3373] [INSPIRE].
J. Perz, P. Smyth, T. Van Riet and B. Vercnocke, First-order flow equations for extremal and non-extremal black holes, JHEP 03 (2009) 150 [arXiv:0810.1528] [INSPIRE].
P. Galli, K. Goldstein, S. Katmadas and J. Perz, First-order flows and stabilisation equations for non-BPS extremal black holes, JHEP 06 (2011) 070 [arXiv:1012.4020] [INSPIRE].
A. Ceresole, G. Dall’Agata, S. Ferrara and A. Yeranyan, First order flows for N=2 extremal black holes and duality invariants, Nucl. Phys. B 824 (2010) 239 [arXiv:0908.1110] [INSPIRE].
L. Andrianopoli, R. D’Auria, E. Orazi and M. Trigiante, First order description of black holes in moduli space, JHEP 11 (2007) 032 [arXiv:0706.0712] [INSPIRE].
L. Andrianopoli, R. D’Auria, E. Orazi and M. Trigiante, First Order Description of D=4 static Black Holes and the Hamilton-Jacobi equation, Nucl. Phys. B 833 (2010) 1 [arXiv:0905.3938] [INSPIRE].
A. Ceresole, G. Dall’Agata, R. Kallosh and A. Van Proeyen, Hypermultiplets, domain walls and supersymmetric attractors, Phys. Rev. D 64 (2001) 104006 [hep-th/0104056] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, An extremization principle for the entropy of rotating BPS black holes in AdS5, JHEP 07 (2017) 106 [arXiv:1705.05383] [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].
S.L. Cacciatori and D. Klemm, Supersymmetric AdS(4) black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926] [INSPIRE].
N. Halmagyi, Static BPS black holes in AdS4 with general dyonic charges, JHEP 03 (2015) 032 [arXiv:1408.2831] [INSPIRE].
K. Hristov, S. Katmadas and C. Toldo, Rotating attractors and BPS black holes in AdS4, JHEP 01 (2019) 199 [arXiv:1811.00292] [INSPIRE].
J.B. Gutowski and H.S. Reall, Supersymmetric AdS(5) black holes, JHEP 02 (2004) 006 [hep-th/0401042] [INSPIRE].
J.B. Gutowski and H.S. Reall, General supersymmetric AdS(5) black holes, JHEP 04 (2004) 048 [hep-th/0401129] [INSPIRE].
H.K. Kunduri, J. Lucietti and H.S. Reall, Supersymmetric multi-charge AdS(5) black holes, JHEP 04 (2006) 036 [hep-th/0601156] [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].
M. Cvetic, G.W. Gibbons, H. Lu and C.N. Pope, Rotating black holes in gauged supergravities: Thermodynamics, supersymmetric limits, topological solitons and time machines, hep-th/0504080 [INSPIRE].
M. Huebscher, P. Meessen, T. Ortin and S. Vaula, N=2 Einstein-Yang-Mills’s BPS solutions, JHEP 09 (2008) 099 [arXiv:0806.1477] [INSPIRE].
S. Bellucci, S. Ferrara, A. Marrani and A. Yeranyan, d=4 Black Hole Attractors in N=2 Supergravity with Fayet-Iliopoulos Terms, Phys. Rev. D 77 (2008) 085027 [arXiv:0802.0141] [INSPIRE].
D. Cassani et al., A Special road to AdS vacua, JHEP 02 (2010) 027 [arXiv:0911.2708] [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].
K. Hristov and S. Vandoren, Static supersymmetric black holes in AdS4 with spherical symmetry, JHEP 04 (2011) 047 [arXiv:1012.4314] [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].
N. Bobev, F.F. Gautason and K. Parmentier, Holographic Uniformization and Black Hole Attractors, JHEP 06 (2020) 095 [arXiv:2004.05110] [INSPIRE].
S.M. Hosseini, K. Hristov, A. Passias and A. Zaffaroni, 6D attractors and black hole microstates, JHEP 12 (2018) 001 [arXiv:1809.10685] [INSPIRE].
A. Cabo-Bizet et al., Entropy functional and the holographic attractor mechanism, JHEP 05 (2018) 155 [arXiv:1712.01849] [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].
K. Hristov, Dimensional reduction of BPS attractors in AdS gauged supergravities, JHEP 12 (2014) 066 [arXiv:1409.8504] [INSPIRE].
S. Kachru, R. Kallosh and M. Shmakova, Generalized Attractor Points in Gauged Supergravity, Phys. Rev. D 84 (2011) 046003 [arXiv:1104.2884] [INSPIRE].
S. Chimento, D. Klemm and N. Petri, Supersymmetric black holes and attractors in gauged supergravity with hypermultiplets, JHEP 06 (2015) 150 [arXiv:1503.09055] [INSPIRE].
D. Astesiano, S.L. Cacciatori and A. Marrani, Black hole attractors and U(1) Fayet-Iliopoulos gaugings: analysis and classification, JHEP 04 (2022) 099 [arXiv:2112.04962] [INSPIRE].
N.V. Suryanarayana and M.C. Wapler, Charges from Attractors, Class. Quant. Grav. 24 (2007) 5047 [arXiv:0704.0955] [INSPIRE].
N.H. Rodríguez and M.J. Rodriguez, First law for Kerr Taub-NUT AdS black holes, JHEP 10 (2022) 044 [arXiv:2112.00780] [INSPIRE].
D. Kastor, Komar Integrals in Higher (and Lower) Derivative Gravity, Class. Quant. Grav. 25 (2008) 175007 [arXiv:0804.1832] [INSPIRE].
D. Kastor, S. Ray and J. Traschen, Enthalpy and the Mechanics of AdS Black Holes, Class. Quant. Grav. 26 (2009) 195011 [arXiv:0904.2765] [INSPIRE].
A. Magnon, On Komar integrals in asymptotically anti-de Sitter space-times, J. Math. Phys. 26 (1985) 3112 [INSPIRE].
T. Ortín, Komar integrals for theories of higher order in the Riemann curvature and black-hole chemistry, JHEP 08 (2021) 023 [arXiv:2104.10717] [INSPIRE].
P.A. Cano and M. David, The extremal Kerr entropy in higher-derivative gravities, JHEP 05 (2023) 219 [arXiv:2303.13286] [INSPIRE].
P. Ntokos and I. Papadimitriou, Black hole superpotential as a unifying entropy function and BPS thermodynamics, JHEP 03 (2022) 058 [arXiv:2112.05954] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, The Geometry of Supersymmetric Partition Functions, JHEP 01 (2014) 124 [arXiv:1309.5876] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, From Rigid Supersymmetry to Twisted Holomorphic Theories, Phys. Rev. D 90 (2014) 085006 [arXiv:1407.2598] [INSPIRE].
J. Markeviciute and J.E. Santos, Evidence for the existence of a novel class of supersymmetric black holes with AdS5×S5 asymptotics, Class. Quant. Grav. 36 (2019) 02LT01 [arXiv:1806.01849] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
D. Cassani, A. Ruipérez and E. Turetta, Boundary terms and conserved charges in higher-derivative gauged supergravity, JHEP 06 (2023) 203 [arXiv:2304.06101] [INSPIRE].
M. Gunaydin, G. Sierra and P.K. Townsend, The Geometry of N=2 Maxwell-Einstein Supergravity and Jordan Algebras, Nucl. Phys. B 242 (1984) 244 [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].
S. Bhattacharyya, S. Minwalla and K. Papadodimas, Small Hairy Black Holes in AdS5xS5, JHEP 11 (2011) 035 [arXiv:1005.1287] [INSPIRE].
J. Markeviciute and J.E. Santos, Hairy black holes in AdS5 × S5, JHEP 06 (2016) 096 [arXiv:1602.03893] [INSPIRE].
O.J.C. Dias, P. Mitra and J.E. Santos, New phases of \( \mathcal{N} \) = 4 SYM at finite chemical potential, JHEP 05 (2023) 053 [arXiv:2207.07134] [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].
F. Benini and E. Milan, A Bethe Ansatz type formula for the superconformal index, Commun. Math. Phys. 376 (2020) 1413 [arXiv:1811.04107] [INSPIRE].
S. Choi, J. Kim, S. Kim and J. Nahmgoong, Large AdS black holes from QFT, arXiv:1810.12067 [INSPIRE].
A. Cabo-Bizet and S. Murthy, Supersymmetric phases of 4d \( \mathcal{N} \) = 4 SYM at large N, JHEP 09 (2020) 184 [arXiv:1909.09597] [INSPIRE].
N. Bobev, K. Hristov and V. Reys, AdS5 holography and higher-derivative supergravity, JHEP 04 (2022) 088 [arXiv:2112.06961] [INSPIRE].
D. Cassani, A. Ruipérez and E. Turetta, Corrections to AdS5 black hole thermodynamics from higher-derivative supergravity, JHEP 11 (2022) 059 [arXiv:2208.01007] [INSPIRE].
J.T. Liu and R.J. Saskowski, Four-derivative corrections to minimal gauged supergravity in five dimensions, JHEP 05 (2022) 171 [arXiv:2201.04690] [INSPIRE].
G. Kántor, C. Papageorgakis and P. Richmond, AdS7 black-hole entropy and 5D \( \mathcal{N} \) = 2 Yang-Mills, JHEP 01 (2020) 017 [arXiv:1907.02923] [INSPIRE].
D.D.K. Chow, Charged rotating black holes in six-dimensional gauged supergravity, Class. Quant. Grav. 27 (2010) 065004 [arXiv:0808.2728] [INSPIRE].
Acknowledgments
We thank Nikolay Bobev, Pablo Cano, Mirjam Cvetic, Alan Fukelman, Luca Illiesiu, Sameer Murthy and Enrico Turetta for valuable discussions. FL thanks the Simons Foundation for support through a sabbatical fellowship. He also thanks Stanford Institute for Theoretical Physics for hospitality and support in the course of the sabbatical. MD thanks CERN for hospitality in the final stages of this work and is especially thankful for Alejandro Cabo-Bizet for letting her borrow an adaptor for her laptop charger to complete the finishing touches of the paper. MD is supported in part by the NSF Graduate Research Fellowship Program under NSF Grant Number: DGE 1256260 and by KU Leuven C1 grant ZKD1118 C16/16/005, and by the Research Programme of The Research Foundation — Flanders (FWO) grant G0F9516N. NE is supported in part by the Leinweber Graduate Fellowship. This work was supported in part by the U.S. Department of Energy under grant DE-SC0007859.
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: 2306.05206
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
David, M., Ezroura, N. & Larsen, F. The attractor flow for AdS5 black holes in \( \mathcal{N} \) = 2 gauged supergravity. J. High Energ. Phys. 2023, 90 (2023). https://doi.org/10.1007/JHEP08(2023)090
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2023)090