Abstract
In this note we analyze the BPS black hole equations in extended supergravities and we find two interesting relations involving first and second derivatives of combinations of the central charges. One relation is a new identity that solely relies on the geometric properties of the scalar manifolds of extended supergravity theories. The other relation is a generalization of a scalar weak gravity conjecture relation conjectured by Palti and uses properties of the underlying black hole solution. We also provide for the first time an explicit covariant construction of the BPS squared action for such solutions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Vafa, The String landscape and the swampland, hep-th/0509212 [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The String landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
E. Palti, The Swampland: Introduction and Review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].
E. Palti, The Weak Gravity Conjecture and Scalar Fields, JHEP 08 (2017) 034 [arXiv:1705.04328] [INSPIRE].
D. Lüst and E. Palti, Scalar Fields, Hierarchical UV/IR Mixing and The Weak Gravity Conjecture, JHEP 02 (2018) 040 [arXiv:1709.01790] [INSPIRE].
T.W. Grimm, E. Palti and I. Valenzuela, Infinite Distances in Field Space and Massless Towers of States, JHEP 08 (2018) 143 [arXiv:1802.08264] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Tensionless Strings and the Weak Gravity Conjecture, JHEP 10 (2018) 164 [arXiv:1808.05958] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, A Stringy Test of the Scalar Weak Gravity Conjecture, Nucl. Phys. B 938 (2019) 321 [arXiv:1810.05169] [INSPIRE].
E. Gonzalo and L.E. Ibáñez, A Strong Scalar Weak Gravity Conjecture and Some Implications, JHEP 08 (2019) 118 [arXiv:1903.08878] [INSPIRE].
S. Brahma and M.W. Hossain, Relating the scalar weak gravity conjecture and the swampland distance conjecture for an accelerating universe, Phys. Rev. D 100 (2019) 086017 [arXiv:1904.05810] [INSPIRE].
S. Shirai and M. Yamazaki, Is Gravity the Weakest Force?, arXiv:1904.10577 [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Repulsive Forces and the Weak Gravity Conjecture, JHEP 10 (2019) 055 [arXiv:1906.02206] [INSPIRE].
A. Kusenko, V. Takhistov, M. Yamada and M. Yamazaki, Fundamental Forces and Scalar Field Dynamics in the Early Universe, arXiv:1908.10930 [INSPIRE].
B. Freivogel, T. Gasenzer, A. Hebecker and S. Leonhardt, A Conjecture on the Minimal Size of Bound States, arXiv:1912.09485 [INSPIRE].
L. Ibáñez, On towers and scalars, talk at String Phenomenology 2019, CERN, 24–28 June 2019 [https://indico.cern.ch/event/782251/contributions/3441881/].
S. Bellucci, S. Ferrara and A. Marrani, Supersymmetric mechanics. Vol. 2: The attractor mechanism and space time singularities, Lect. Notes Phys. 701 (2006) 1 [INSPIRE].
A. Font, A. Herráez and L.E. Ibáñez, The Swampland Distance Conjecture and Towers of Tensionless Branes, JHEP 08 (2019) 044 [arXiv:1904.05379] [INSPIRE].
A. Ceresole, R. D’Auria, S. Ferrara and A. Van Proeyen, Duality transformations in supersymmetric Yang-Mills theories coupled to supergravity, Nucl. Phys. B 444 (1995) 92 [hep-th/9502072] [INSPIRE].
S. Ferrara, C.A. Savoy and B. Zumino, General Massive Multiplets in Extended Supersymmetry, Phys. Lett. 100B (1981) 393 [INSPIRE].
L. Andrianopoli, R. D’Auria and S. Ferrara, U duality and central charges in various dimensions revisited, Int. J. Mod. Phys. A 13 (1998) 431 [hep-th/9612105] [INSPIRE].
L. Andrianopoli, R. D’Auria and S. Ferrara, Central extension of extended supergravities in diverse dimensions, Int. J. Mod. Phys. A 12 (1997) 3759 [hep-th/9608015] [INSPIRE].
L. Andrianopoli, R. D’Auria and S. Ferrara, U invariants, black hole entropy and fixed scalars, Phys. Lett. B 403 (1997) 12 [hep-th/9703156] [INSPIRE].
G. Dall’Agata, Black holes in supergravity: flow equations and duality, Springer Proc. Phys. 142 (2013) 1 [arXiv:1106.2611] [INSPIRE].
L. Castellani, A. Ceresole, S. Ferrara, R. D’Auria, P. Fré and E. Maina, The Complete N = 3 Matter Coupled Supergravity, Nucl. Phys. B 268 (1986) 317 [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].
S. Ferrara, A. Gnecchi and A. Marrani, d = 4 Attractors, Effective Horizon Radius and Fake Supergravity, Phys. Rev. D 78 (2008) 065003 [arXiv:0806.3196] [INSPIRE].
E. Bergshoeff, I.G. Koh and E. Sezgin, Coupling of Yang-Mills to N = 4, D = 4 Supergravity, Phys. Lett. 155B (1985) 71 [INSPIRE].
J. Schon and M. Weidner, Gauged N = 4 supergravities, JHEP 05 (2006) 034 [hep-th/0602024] [INSPIRE].
K. Behrndt, R. Kallosh, J. Rahmfeld, M. Shmakova and W.K. Wong, STU black holes and string triality, Phys. Rev. D 54 (1996) 6293 [hep-th/9608059] [INSPIRE].
A. Ceresole and G. Dall’Agata, Flow Equations for Non-BPS Extremal Black Holes, JHEP 03 (2007) 110 [hep-th/0702088] [INSPIRE].
L. Andrianopoli, R. D’Auria, S. Ferrara and M. Trigiante, Extremal black holes in supergravity, Lect. Notes Phys. 737 (2008) 661 [hep-th/0611345] [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: 2001.10542
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
Dall’Agata, G., Morittu, M. Covariant formulation of BPS black holes and the scalar weak gravity conjecture. J. High Energ. Phys. 2020, 192 (2020). https://doi.org/10.1007/JHEP03(2020)192
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2020)192