Abstract
We establish an attractor mechanism for the horizon metric of asymptotically locally AdS4 supersymmetric black holes. The horizon is a smooth Riemann surface with arbitrary metric at asymptotic infinity which is fixed to the constant curvature metric in the near horizon region. We show how this mechanism is realized for four-dimensional \( \mathcal{N} \) = 2 gauged supergravity coupled to vector multiplets by focusing on the STU model. A similar analysis is performed for gauged supergravity theories in five, six, and seven dimen- sions where we establish the same mechanism by extending previous results on holographic uniformization.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
M. Bershadsky, C. Vafa and V. Sadov, D-branes and topological field theories, Nucl. Phys. B 463 (1996) 420 [hep-th/9511222] [INSPIRE].
J.P. Gauntlett, Branes, calibrations and supergravity, Clay Math. Proc. 3 (2004) 79 [hep-th/0305074] [INSPIRE].
M. Naka, Various wrapped branes from gauged supergravities, hep-th/0206141 [INSPIRE].
N. Bobev and P.M. Crichigno, Universal RG flows across dimensions and holography, JHEP 12 (2017) 065 [arXiv:1708.05052] [INSPIRE].
E. Witten, Topological quantum field theory, Commun. Math. Phys. 117 (1988) 353 [INSPIRE].
M.T. Anderson, C. Beem, N. Bobev and L. Rastelli, Holographic uniformization, Commun. Math. Phys. 318 (2013) 429 [arXiv:1109.3724] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
D. Gaiotto, G.W. Moore and Y. Tachikawa, On 6d N = (2, 0) theory compactified on a Riemann surface with finite area, PTEP 2013 (2013) 013B03 [arXiv:1110.2657] [INSPIRE].
S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) R5412 [hep-th/9508072] [INSPIRE].
A. Strominger, Macroscopic entropy of N = 2 extremal black holes, Phys. Lett. B 383 (1996) 39 [hep-th/9602111] [INSPIRE].
S. Ferrara and R. Kallosh, Supersymmetry and attractors, Phys. Rev. D 54 (1996) 1514 [hep-th/9602136] [INSPIRE].
A. Sen, Black hole entropy function, attractors and precision counting of microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].
J.D. Bekenstein, Black hole hair: 25-years after, in Physics. Proceedings, 2nd International A.D. Sakharov conference, Moscow, Russia, 20–24 May 1996, pg. 216 [gr-qc/9605059] [INSPIRE].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
S.L. Cacciatori and D. Klemm, Supersymmetric AdS4 black holes and attractors, JHEP 01 (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, 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].
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].
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].
A. Zaffaroni, Lectures on AdS black holes, holography and localization, arXiv:1902.07176 [INSPIRE].
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].
C. Closset and H. Kim, Comments on twisted indices in 3d supersymmetric gauge theories, JHEP 08 (2016) 059 [arXiv:1605.06531] [INSPIRE].
N. Bobev, P. Bomans and F.F. Gautason, Wrapped branes and punctured horizons, JHEP 06 (2020) 011 [arXiv:1912.04779] [INSPIRE].
D.Z. Freedman and A.K. Das, Gauge internal symmetry in extended supergravity, Nucl. Phys. B 120 (1977) 221 [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, Model of supergravity with minimal electromagnetic interaction, LEBEDEV-76-197, (1976) [INSPIRE].
M.M. Caldarelli and D. Klemm, Supersymmetry of anti-de Sitter black holes, Nucl. Phys. B 545 (1999) 434 [hep-th/9808097] [INSPIRE].
L.J. Romans, Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory, Nucl. Phys. B 383 (1992) 395 [hep-th/9203018] [INSPIRE].
J.P. Gauntlett, N. Kim, S. Pakis and D. Waldram, Membranes wrapped on holomorphic curves, Phys. Rev. D 65 (2002) 026003 [hep-th/0105250] [INSPIRE].
R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. 35 (1994) 4217 [INSPIRE].
C. Fefferman and C.R. Graham, Conformal invariants, in Élie Cartan et les mathématiques d’aujourdui, Asterisque, France (1985), pg. 95.
M.T. Anderson, Geometric aspects of the AdS/CFT correspondence, IRMA Lect. Math. Theor. Phys. 8 (2005) 1 [hep-th/0403087] [INSPIRE].
M. Cvetič, S.S. Gubser, H. Lü and C.N. Pope, Symmetric potentials of gauged supergravities in diverse dimensions and Coulomb branch of gauge theories, Phys. Rev. D 62 (2000) 086003 [hep-th/9909121] [INSPIRE].
R.C. Myers and O. Tafjord, Superstars and giant gravitons, JHEP 11 (2001) 009 [hep-th/0109127] [INSPIRE].
S.S. Gubser, Curvature singularities: the good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [INSPIRE].
R. D’Auria, E. Maina, T. Regge and P. Fré, Geometrical first order supergravity in five space-time dimensions, Annals Phys. 135 (1981) 237 [INSPIRE].
A.H. Chamseddine and H. Nicolai, Coupling the SO(2) supergravity through dimensional reduction, Phys. Lett. B 96 (1980) 89 [Erratum ibid. B 785 (2018) 631] [arXiv:1808.08955] [INSPIRE].
D. Klemm and W.A. Sabra, Supersymmetry of black strings in D = 5 gauged supergravities, Phys. Rev. D 62 (2000) 024003 [hep-th/0001131] [INSPIRE].
F. Benini and N. Bobev, Two-dimensional SCFTs from wrapped branes and c-extremization, JHEP 06 (2013) 005 [arXiv:1302.4451] [INSPIRE].
F. Benini, N. Bobev and P.M. Crichigno, Two-dimensional SCFTs from D3-branes, JHEP 07 (2016) 020 [arXiv:1511.09462] [INSPIRE].
L.J. Romans, The F (4) gauged supergravity in six-dimensions, Nucl. Phys. B 269 (1986) 691 [INSPIRE].
C. Núñez, I.Y. Park, M. Schvellinger and T.A. Tran, Supergravity duals of gauge theories from F (4) gauged supergravity in six-dimensions, JHEP 04 (2001) 025 [hep-th/0103080] [INSPIRE].
P.K. Townsend and P. van Nieuwenhuizen, Gauged seven-dimensional supergravity, Phys. Lett. B 125 (1983) 41 [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].
I. Bah, C. Beem, N. Bobev and B. Wecht, AdS/CFT dual pairs from M5-branes on Riemann surfaces, Phys. Rev. D 85 (2012) 121901 [arXiv:1112.5487] [INSPIRE].
I. Bah, C. Beem, N. Bobev and B. Wecht, Four-dimensional SCFTs from M5-branes, JHEP 06 (2012) 005 [arXiv:1203.0303] [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].
M. Pernici, K. Pilch and P. van Nieuwenhuizen, Gauged maximally extended supergravity in seven-dimensions, Phys. Lett. B 143 (1984) 103 [INSPIRE].
J.T. Liu and R. Minasian, Black holes and membranes in AdS7 , Phys. Lett. B 457 (1999) 39 [hep-th/9903269] [INSPIRE].
M.M. Caldarelli and D. Klemm, All supersymmetric solutions of N = 2, D = 4 gauged supergravity, JHEP 09 (2003) 019 [hep-th/0307022] [INSPIRE].
J.P. Gauntlett and J.B. Gutowski, All supersymmetric solutions of minimal gauged supergravity in five-dimensions, Phys. Rev. D 68 (2003) 105009 [Erratum ibid. D 70 (2004) 089901] [hep-th/0304064] [INSPIRE].
M. Cariglia and O.A.P. Mac Conamhna, The general form of supersymmetric solutions of N = (1, 0) U(1) and SU(2) gauged supergravities in six-dimensions, Class. Quant. Grav. 21 (2004) 3171 [hep-th/0402055] [INSPIRE].
O.A.P. Mac Conamhna, Refining G-structure classifications, Phys. Rev. D 70 (2004) 105024 [hep-th/0408203] [INSPIRE].
K. Hristov, S. Katmadas and C. Toldo, Rotating attractors and BPS black holes in AdS4 , JHEP 01 (2019) 199 [arXiv:1811.00292] [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].
C. Beem, N. Bobev, F.F. Gautason and K. Parmentier, Holographic geometrization, work in progress.
M. Fluder, Kähler uniformization from holographic renormalization group flows of M5-branes, JHEP 08 (2018) 046 [arXiv:1710.09479] [INSPIRE].
M. Fluder, 4d N = 1/2d Yang-Mills duality in holography, JHEP 08 (2018) 038 [arXiv:1712.06596] [INSPIRE].
D. Friedan, Nonlinear models in 2 + ϵ dimensions, Phys. Rev. Lett. 45 (1980) 1057 [INSPIRE].
G. Perelman, The entropy formula for the Ricci flow and its geometric applications, math.DG/0211159.
A. Cabo-Bizet, U. Kol, L.A. Pando Zayas, I. Papadimitriou and V. Rathee, Entropy functional and the holographic attractor mechanism, JHEP 05 (2018) 155 [arXiv:1712.01849] [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].
E. D’Hoker and P. Kraus, Magnetic brane solutions in AdS, JHEP 10 (2009) 088 [arXiv:0908.3875] [INSPIRE].
A. Almuhairi, AdS3 and AdS2 magnetic brane solutions, arXiv:1011.1266 [INSPIRE].
A. Almuhairi and J. Polchinski, Magnetic AdS×R2 : supersymmetry and stability, arXiv:1108.1213 [INSPIRE].
A. Donos, J.P. Gauntlett and C. Pantelidou, Magnetic and electric AdS solutions in string- and M-theory, Class. Quant. Grav. 29 (2012) 194006 [arXiv:1112.4195] [INSPIRE].
N. Bobev, unpublished notes, (2011).
A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional nearly anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
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
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: 2004.05110
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Bobev, N., Gautason, F.F. & Parmentier, K. Holographic uniformization and black hole attractors. J. High Energ. Phys. 2020, 95 (2020). https://doi.org/10.1007/JHEP06(2020)095
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2020)095