Abstract
We consider the shift of charge-to-mass ratio for extremal black holes in the context of effective field theory, motivated by the Weak Gravity Conjecture. We constrain extremality corrections in different regimes subject to unitarity and causality constraints. In the asymptotic IR, we demonstrate that for any supersymmetric theory in flat space, and for all minimally coupled theories, logarithmic running at one loop pushes the Wilson coefficient of certain four-derivative operators to be larger at lower energies, guaranteeing the existence of sufficiently large black holes with Q > M. We identify two exceptional cases of nonsupersymmetric theories involving large numbers of light states and Planck-scale nonminimal couplings, in which the sign of the running is reversed, leading to black holes with negative corrections to Q/M in the deep IR, but argue that these do not rule out extremal black holes as the requisite charged states for the WGC. We separately show that causality and unitarity imply that the leading threshold corrections to the effective action from integrating out massive states, in any weakly coupled theory, can be written as a sum of squares and is manifestly positive for black hole backgrounds. Quite beautifully, the shift in the extremal Q/M ratio is directly proportional to the shift in the on-shell action, guaranteeing that these threshold corrections push Q > M in compliance with the WGC. Our results apply for black holes with or without dilatonic coupling and charged under any number of U(1)s.
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].
H. Ooguri and C. Vafa, On the geometry of the string landscape and the swampland, Nucl. Phys. B 766 (2007) 21 [hep-th/0605264] [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].
L. Susskind, Trouble for remnants, hep-th/9501106 [INSPIRE].
S.B. Giddings, Black holes and massive remnants, Phys. Rev. D 46 (1992) 1347 [hep-th/9203059] [INSPIRE].
G. ’t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
R. Bousso, The holographic principle, Rev. Mod. Phys. 74 (2002) 825 [hep-th/0203101] [INSPIRE].
T. Banks, M. Johnson and A. Shomer, A note on gauge theories coupled to gravity, JHEP 09 (2006) 049 [hep-th/0606277] [INSPIRE].
Y. Kats, L. Motl and M. Padi, Higher-order corrections to mass-charge relation of extremal black holes, JHEP 12 (2007) 068 [hep-th/0606100] [INSPIRE].
C. Cheung, J. Liu and G.N. Remmen, Proof of the weak gravity conjecture from black hole entropy, JHEP 10 (2018) 004 [arXiv:1801.08546] [INSPIRE].
C. Cheung, J. Liu and G.N. Remmen, Entropy bounds on effective field theory from rotating dyonic black holes, Phys. Rev. D 100 (2019) 046003 [arXiv:1903.09156] [INSPIRE].
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, The EFT-Hedron, JHEP 05 (2021) 259 [arXiv:2012.15849] [INSPIRE].
C. Cheung and G.N. Remmen, Infrared consistency and the weak gravity conjecture, JHEP 12 (2014) 087 [arXiv:1407.7865] [INSPIRE].
B. Bellazzini, C. Cheung and G.N. Remmen, Quantum gravity constraints from unitarity and analyticity, Phys. Rev. D 93 (2016) 064076 [arXiv:1509.00851] [INSPIRE].
B. Bellazzini, M. Lewandowski and J. Serra, Positivity of amplitudes, weak gravity conjecture, and modified gravity, Phys. Rev. Lett. 123 (2019) 251103 [arXiv:1902.03250] [INSPIRE].
Y. Hamada, T. Noumi and G. Shiu, Weak gravity conjecture from unitarity and causality, Phys. Rev. Lett. 123 (2019) 051601 [arXiv:1810.03637] [INSPIRE].
S. Caron-Huot, D. Mazac, L. Rastelli and D. Simmons-Duffin, Sharp Boundaries for the Swampland, JHEP 07 (2021) 110 [arXiv:2102.08951] [INSPIRE].
P.A. Cano, T. Ortín and P.F. Ramirez, On the extremality bound of stringy black holes, JHEP 02 (2020) 175 [arXiv:1909.08530] [INSPIRE].
P.A. Cano, S. Chimento, R. Linares, T. Ortín and P.F. Ramírez, α′ corrections of Reissner-Nordström black holes, JHEP 02 (2020) 031 [arXiv:1910.14324] [INSPIRE].
S. Deser and P. van Nieuwenhuizen, One loop divergences of quantized Einstein-Maxwell fields, Phys. Rev. D 10 (1974) 401 [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Scalar one loop integrals, Nucl. Phys. B 153 (1979) 365 [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated one loop integrals, Phys. Lett. B 302 (1993) 299 [Erratum ibid. 318 (1993) 649] [hep-ph/9212308] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated pentagon integrals, Nucl. Phys. B 412 (1994) 751 [hep-ph/9306240] [INSPIRE].
D.C. Dunbar and P.S. Norridge, Infinities within graviton scattering amplitudes, Class. Quant. Grav. 14 (1997) 351 [hep-th/9512084] [INSPIRE].
D. Forde, Direct extraction of one-loop integral coefficients, Phys. Rev. D 75 (2007) 125019 [arXiv:0704.1835] [INSPIRE].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].
R. Britto, E. Buchbinder, F. Cachazo and B. Feng, One-loop amplitudes of gluons in SQCD, Phys. Rev. D 72 (2005) 065012 [hep-ph/0503132] [INSPIRE].
D.A. McGady and L. Rodina, Higher-spin massless S-matrices in four-dimensions, Phys. Rev. D 90 (2014) 084048 [arXiv:1311.2938] [INSPIRE].
P. van Nieuwenhuizen and J.A.M. Vermaseren, One loop divergences in the quantum theory of supergravity, Phys. Lett. B 65 (1976) 263 [INSPIRE].
A.M. Charles, The weak gravity conjecture, RG flows, and supersymmetry, arXiv:1906.07734 [INSPIRE].
T. Banks, Cosmological breaking of supersymmetry?, Int. J. Mod. Phys. A 16 (2001) 910 [hep-th/0007146] [INSPIRE].
G. Dvali, Black holes and large N species solution to the hierarchy problem, Fortsch. Phys. 58 (2010) 528 [arXiv:0706.2050] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos and S. Kachru, Predictive landscapes and new physics at a TeV, hep-th/0501082 [INSPIRE].
S. Dimopoulos, S. Kachru, J. McGreevy and J.G. Wacker, N-flation, JCAP 08 (2008) 003 [hep-th/0507205] [INSPIRE].
C. Cheung and G.N. Remmen, Naturalness and the weak gravity conjecture, Phys. Rev. Lett. 113 (2014) 051601 [arXiv:1402.2287] [INSPIRE].
H.S. Reall and J.E. Santos, Higher derivative corrections to Kerr black hole thermodynamics, JHEP 04 (2019) 021 [arXiv:1901.11535] [INSPIRE].
G. Goon and R. Penco, Universal relation between corrections to entropy and extremality, Phys. Rev. Lett. 124 (2020) 101103 [arXiv:1909.05254] [INSPIRE].
D.J. Gross and E. Witten, Superstring modifications of Einstein’s equations, Nucl. Phys. B 277 (1986) 1 [INSPIRE].
A. Gruzinov and M. Kleban, Causality constrains higher curvature corrections to gravity, Class. Quant. Grav. 24 (2007) 3521 [hep-th/0612015] [INSPIRE].
D. Garfinkle, G.T. Horowitz and A. Strominger, Charged black holes in string theory, Phys. Rev. D 43 (1991) 3140 [Erratum ibid. 45 (1992) 3888] [INSPIRE].
A.P. Porfyriadis and G.N. Remmen, Horizon acoustics of the GHS black hole and the spectrum of AdS2, JHEP 10 (2021) 142 [arXiv:2106.10282] [INSPIRE].
C. Herdeiro, E. Radu and K. Uzawa, De-singularizing the extremal GMGHS black hole via higher derivatives corrections, Phys. Lett. B 818 (2021) 136357 [arXiv:2103.00884] [INSPIRE].
C. Zhang and S.-Y. Zhou, Convex geometry perspective on the (standard model) effective field theory space, Phys. Rev. Lett. 125 (2020) 201601 [arXiv:2005.03047] [INSPIRE].
S. Andriolo, T.-C. Huang, T. Noumi, H. Ooguri and G. Shiu, Duality and axionic weak gravity, Phys. Rev. D 102 (2020) 046008 [arXiv:2004.13721] [INSPIRE].
O. Aharony and E. Palti, Convexity of charged operators in CFTs and the weak gravity conjecture, Phys. Rev. D 104 (2021) 126005 [arXiv:2108.04594] [INSPIRE].
C.F.E. Holzhey and F. Wilczek, Black holes as elementary particles, Nucl. Phys. B 380 (1992) 447 [hep-th/9202014] [INSPIRE].
G.J. Loges, T. Noumi and G. Shiu, Thermodynamics of 4D dilatonic black holes and the weak gravity conjecture, Phys. Rev. D 102 (2020) 046010 [arXiv:1909.01352] [INSPIRE].
V. Chandrasekaran, G.N. Remmen and A. Shahbazi-Moghaddam, Higher-point positivity, JHEP 11 (2018) 015 [arXiv:1804.03153] [INSPIRE].
I. Huet, M. Rausch de Traubenberg and C. Schubert, The Euler-Heisenberg Lagrangian beyond one loop, Int. J. Mod. Phys. Conf. Ser. 14 (2012) 383 [arXiv:1112.1049] [INSPIRE].
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: 2109.13937
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
Arkani-Hamed, N., Huang, Yt., Liu, JY. et al. Causality, unitarity, and the weak gravity conjecture. J. High Energ. Phys. 2022, 83 (2022). https://doi.org/10.1007/JHEP03(2022)083
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2022)083