Abstract
Freudenthal duality in N = 2, D = 4 ungauged supergravity is generated by an anti-involutive operator that acts on the electromagnetic fluxes, and results to be a symmetry of the Bekenstein-Hawking entropy. We show that, with a suitable extension, this duality can be generalized to the abelian gauged case as well, even in presence of hypermultiplets. By defining Freudenthal duality along the scalar flow, one can prove that two configurations of charges and gaugings linked by the Freudenthal operator share the same set of values of the scalar fields at the black hole horizon. Consequently, Freudenthal duality is promoted to a nonlinear symmetry of the black hole entropy. We explicitly show this invariance for the model with prepotential F = −iX 0 X 1 and Fayet-Iliopoulos gauging.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
S. Ferrara and R. Kallosh, Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525 [hep-th/9603090] [INSPIRE].
S. Ferrara, G.W. Gibbons and R. Kallosh, Black holes and critical points in moduli space, Nucl. Phys. B 500 (1997) 75 [hep-th/9702103] [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].
S.L. Cacciatori and D. Klemm, Supersymmetric AdS 4 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].
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].
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 AdS 4 with spherical symmetry, JHEP 04 (2011) 047 [arXiv:1012.4314] [INSPIRE].
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] [INSPIRE].
C. Toldo and S. Vandoren, Static nonextremal AdS4 black hole solutions, JHEP 09 (2012) 048 [arXiv:1207.3014] [INSPIRE].
K. Hristov, S. Katmadas and V. Pozzoli, Ungauging black holes and hidden supercharges, JHEP 01 (2013) 110 [arXiv:1211.0035] [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, JHEP 03 (2013) 088 [arXiv:1211.1966] [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].
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].
D. Klemm, A. Marrani, N. Petri and C. Santoli, BPS black holes in a non-homogeneous deformation of the STU model of N = 2, D = 4 gauged supergravity, JHEP 09 (2015) 205 [arXiv:1507.05553] [INSPIRE].
N. Halmagyi, M. Petrini and A. Zaffaroni, BPS black holes in AdS 4 from M-theory, JHEP 08 (2013) 124 [arXiv:1305.0730] [INSPIRE].
D. Klemm, N. Petri and M. Rabbiosi, Symplectically invariant flow equations for N = 2, D = 4 gauged supergravity with hypermultiplets, JHEP 04(2016)008 [arXiv:1602.01334] [INSPIRE].
J. Polchinski and A. Strominger, New vacua for type-II string theory, Phys. Lett. B 388 (1996) 736 [hep-th/9510227] [INSPIRE].
J. Michelson, Compactifications of type IIB strings to four-dimensions with nontrivial classical potential, Nucl. Phys. B 495 (1997) 127 [hep-th/9610151] [INSPIRE].
G. Dall’Agata, Type IIB supergravity compactified on a Calabi-Yau manifold with H fluxes, JHEP 11 (2001) 005 [hep-th/0107264] [INSPIRE].
J.P. Hsu, A. Maloney and A. Tomasiello, Black hole attractors and pure spinors, JHEP 09 (2006) 048 [hep-th/0602142] [INSPIRE].
U.H. Danielsson, N. Johansson and M. Larfors, Stability of flux vacua in the presence of charged black holes, JHEP 09 (2006) 069 [hep-th/0605106] [INSPIRE].
L. Borsten, D. Dahanayake, M.J. Duff and W. Rubens, Black holes admitting a Freudenthal dual, Phys. Rev. D 80 (2009) 026003 [arXiv:0903.5517] [INSPIRE].
R.B. Brown, Groups of type E 7, J. Reine Angew. Math. 236 (1969) 79.
S. Ferrara, A. Marrani, E. Orazi and M. Trigiante, Dualities Near the Horizon, JHEP 11 (2013)056 [arXiv:1305.2057] [INSPIRE].
A. Marrani, Freudenthal Duality in Gravity: from Groups of Type E 7 to Pre-Homogeneous Spaces, arXiv:1509.01031 [INSPIRE].
S. Ferrara, A. Marrani and A. Yeranyan, Freudenthal Duality and Generalized Special Geometry, Phys. Lett. B 701 (2011) 640 [arXiv:1102.4857] [INSPIRE].
A. Marrani, C.-X. Qiu, S.-Y.D. Shih, A. Tagliaferro and B. Zumino, Freudenthal Gauge Theory, JHEP 03 (2013) 132 [arXiv:1208.0013] [INSPIRE].
J.J. Fernandez-Melgarejo and E. Torrente-Lujan, N = 2 SUGRA BPS Multi-center solutions, quadratic prepotentials and Freudenthal transformations, JHEP 05 (2014) 081 [arXiv:1310.4182] [INSPIRE].
L. Borsten, M.J. Duff, S. Ferrara and A. Marrani, Freudenthal Dual Lagrangians, Class. Quant. Grav. 30 (2013) 235003 [arXiv:1212.3254] [INSPIRE].
P. Galli, P. Meessen and T. Ortín, The Freudenthal gauge symmetry of the black holes of N = 2, d = 4 supergravity, JHEP 05(2013)011 [arXiv:1211.7296] [INSPIRE].
S. Ferrara, R. Kallosh and A. Marrani, Degeneration of Groups of Type E 7 and Minimal Coupling in Supergravity, JHEP 06 (2012) 074 [arXiv:1202.1290] [INSPIRE].
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].
L. Andrianopoli, R. D’Auria, S. Ferrara and M. Trigiante, Black-hole attractors in N = 1 supergravity, JHEP 07 (2007) 019 [hep-th/0703178] [INSPIRE].
F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS 4 from supersymmetric localization, JHEP 05 (2016) 054 [arXiv:1511.04085] [INSPIRE].
D. Martelli and J. Sparks, AdS 4 /CFT 3 duals from M2-branes at hypersurface singularities and their deformations, JHEP 12 (2009) 017 [arXiv:0909.2036] [INSPIRE].
D.L. Jafferis, Quantum corrections to N = 2 Chern-Simons theories with flavor and their AdS 4 duals, JHEP 08 (2013) 046 [arXiv:0911.4324] [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].
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
ArXiv ePrint: 1701.08536
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
Klemm, D., Marrani, A., Petri, N. et al. Nonlinear symmetries of black hole entropy in gauged supergravity. J. High Energ. Phys. 2017, 13 (2017). https://doi.org/10.1007/JHEP04(2017)013
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2017)013