Abstract
We study static BPS black hole horizons in four dimensional \( \mathcal{N} \) = 2 gauged supergravity coupled to n v -vector multiplets and with an arbitrary cubic prepotential. We work in a symplectically covariant formalism which allows for both electric and magnetic gauging parameters as well as dyonic background charges and obtain the general solution to the BPS equations for horizons of the form AdS 2 × Σ g . In particular this means we solve for the scalar fields as well as the metric of these black holes as a function of the gauging parameters and background charges. When the special Kähler manifold is a symmetric space, our solution is completely explicit and the entropy is related to the familiar quartic invariant. For more general models our solution is implicit up to a set of holomorphic quadratic equations. For particular models which have known embeddings in M-theory, we derive new horizon geometries with dyonic charges and numerically construct black hole solutions. These correspond to M2-branes wrapped on a Riemann surface in a local Calabi-Yau five-fold with internal spin.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.L. Cacciatori and D. Klemm, Supersymmetric AdS 4 black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926].
M.M. Caldarelli and D. Klemm, Supersymmetry of anti-de Sitter black holes, Nucl. Phys. B 545 (1999) 434 [hep-th/9808097].
N. Halmagyi, M. Petrini and A. Zaffaroni, BPS black holes in AdS 4 from M-theory, JHEP 08 (2013) 124 [arXiv:1305.0730].
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].
T. Kimura, Non-supersymmetric extremal RN-AdS black holes in N = 2 gauged supergravity, JHEP 09 (2010) 061 [arXiv:1005.4607].
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].
K. Hristov and S. Vandoren, Static supersymmetric black holes in AdS 4 with spherical symmetry, JHEP 04 (2011) 047 [arXiv:1012.4314].
D. Klemm and O. Vaughan, Nonextremal black holes in gauged supergravity and the real formulation of special geometry, JHEP 01 (2013) 053 [arXiv:1207.2679].
K. Hristov, C. Toldo and S. Vandoren, Phase transitions of magnetic AdS 4 black holes with scalar hair, Phys. Rev. D 88 (2013) 026019 [arXiv:1304.5187].
A. Gnecchi and C. Toldo, On the non-BPS first order flow in N = 2 U(1)-gauged Supergravity, JHEP 03 (2013) 088 [arXiv:1211.1966].
S. Barisch, G.L. Cardoso, M. Haack, S. Nampuri and N.A. Obers, Nernst branes in gauged supergravity, JHEP 11 (2011) 090 [arXiv:1108.0296].
A. Donos, J.P. Gauntlett and C. Pantelidou, Magnetic and electric AdS solutions in string- and M-theory, Class. and Quant. Grav. 29 (2012) 194006 [arXiv:1112.4195].
A. Donos, J.P. Gauntlett and C. Pantelidou, Semi-local quantum criticality in string/M-theory, JHEP 03 (2013) 103 [arXiv:1212.1462].
J. Maldacena and C. Nuñez, Supergravity Description of Field Theories on Curved Manifolds and a no GO Theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018].
J.P. Gauntlett, N. Kim, S. Pakis and D. Waldram, Membranes wrapped on holomorphic curves, Phys. Rev. D 65 (2002) 026003 [hep-th/0105250].
S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) 5412 [hep-th/9508072].
K. Behrndt, D. Lüst and W.A. Sabra, Stationary solutions of N = 2 supergravity, Nucl. Phys. B 510 (1998) 264 [hep-th/9705169].
B. de Wit, H. Samtleben and M. Trigiante, Magnetic charges in local field theory, JHEP 09 (2005) 016 [hep-th/0507289].
B. de Wit and M. van Zalk, Electric and magnetic charges in N = 2 conformal supergravity theories, JHEP 10 (2011) 050 [arXiv:1107.3305].
L. Andrianopoli, M. Bertolini, A. Ceresole, R. D’Auria, S. Ferrara and P. Fré, General matter coupled N = 2 supergravity, Nucl. Phys. B 476 (1996) 397 [hep-th/9603004].
M. Shmakova, Calabi-Yau Black Holes, Phys. Rev. D 56 (1997) 540 [hep-th/9612076].
S. Ferrara and R. Kallosh, Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525 [hep-th/9603090].
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].
B. Pioline, Lectures on black holes, topological strings and quantum attractors, Class. Quant. Grav. 23 (2006) S981 [hep-th/0607227] [INSPIRE].
M. Günaydin, G. Sierra and P. Townsend, The Geometry of N = 2 Maxwell-Einstein Supergravity and Jordan Algebras, Nucl. Phys. B 242 (1984) 244 [INSPIRE].
B. de Wit, F. Vanderseypen and A. Van Proeyen, Symmetry structure of special geometries, Nucl. Phys. B 400 (1993) 463 [hep-th/9210068] [INSPIRE].
N. Halmagyi, work in progress.
M. Duff and J.T. Liu, Anti-de Sitter black holes in gauged N = 8 supergravity, Nucl. Phys. B 554 (1999) 237 [hep-th/9901149] [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].
J.P. Gauntlett, S. Kim, O. Varela and D. Waldram, Consistent supersymmetric Kaluza-Klein truncations with massive modes, JHEP 04 (2009) 102 [arXiv:0901.0676] [INSPIRE].
A. Donos, J.P. Gauntlett, N. Kim and O. Varela, Wrapped M5-branes, consistent truncations and AdS/CMT, JHEP 12 (2010) 003 [arXiv:1009.3805] [INSPIRE].
D. Cassani, P. Koerber and O. Varela, All homogeneous N = 2 M-theory truncations with supersymmetric AdS4 vacua, JHEP 11 (2012) 173 [arXiv:1208.1262] [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
Dedicated to the loving memory of Sue Halmagyi
ArXiv ePrint: 1308.1439
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Halmagyi, N. BPS black hole horizons in N=2 gauged supergravity. J. High Energ. Phys. 2014, 51 (2014). https://doi.org/10.1007/JHEP02(2014)051
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2014)051