Abstract
Positivity bounds coming from consistency of UV scattering amplitudes are not always sufficient to prove the weak gravity conjecture for theories beyond Einstein-Maxwell. Additional ingredients about the UV may be necessary to exclude those regions of parameter space which are naïvely in conflict with the predictions of the weak gravity conjecture. In this paper we explore the consequences of imposing additional symmetries inherited from the UV theory on higher-derivative operators for Einstein-Maxwell-dilaton-axion theory. Using black hole thermodynamics, for a preserved SL(2, ℝ) symmetry we find that the weak gravity conjecture then does follow from positivity bounds. For a preserved O(d, d; ℝ) symmetry we find a simple condition on the two Wilson coefficients which ensures the positivity of corrections to the charge-to-mass ratio and that follows from the null energy condition alone. We find that imposing supersymmetry on top of either of these symmetries gives corrections which vanish identically, as expected for BPS states.
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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].
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].
Y. Hamada, T. Noumi and G. Shiu, Weak gravity conjecture from unitarity and causality, Phys. Rev. Lett. 123 (2019) 051601 [arXiv:1810.03637] [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].
A.M. Charles, The weak gravity conjecture, RG flows, and supersymmetry, arXiv:1906.07734 [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].
G. Goon and R. Penco, Universal relation between corrections to entropy and extremality, Phys. Rev. Lett. 124 (2020) 101103 [arXiv:1909.05254] [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. Cremonini, C.R.T. Jones, J.T. Liu and B. McPeak, Higher-derivative corrections to entropy and the weak gravity conjecture in Anti-de Sitter space, JHEP 09 (2020) 003 [arXiv:1912.11161] [INSPIRE].
S.-W. Wei, K. Yang and Y.-X. Liu, Universal thermodynamic relations with constant corrections for rotating AdS black holes, arXiv:2003.06785 [INSPIRE].
Q. Chen, W. Hong and J. Tao, Universal thermodynamic extremality relations for charged AdS black hole surrounded by quintessence, arXiv:2005.00747 [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].
J. Brown, W. Cottrell, G. Shiu and P. Soler, Fencing in the Swampland: quantum gravity constraints on large field inflation, JHEP 10 (2015) 023 [arXiv:1503.04783] [INSPIRE].
J. Brown, W. Cottrell, G. Shiu and P. Soler, On axionic field ranges, loopholes and the weak gravity conjecture, JHEP 04 (2016) 017 [arXiv:1504.00659] [INSPIRE].
M. Montero, A.M. Uranga and I. Valenzuela, Transplanckian axions!?, JHEP 08 (2015) 032 [arXiv:1503.03886] [INSPIRE].
A. de la Fuente, P. Saraswat and R. Sundrum, Natural inflation and quantum gravity, Phys. Rev. Lett. 114 (2015) 151303 [arXiv:1412.3457] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Weak gravity strongly constrains large-field axion inflation, JHEP 12 (2015) 108 [arXiv:1506.03447] [INSPIRE].
T. Rudelius, Constraints on axion inflation from the weak gravity conjecture, JCAP 09 (2015) 020 [arXiv:1503.00795] [INSPIRE].
D. Junghans, Large-field inflation with multiple axions and the weak gravity conjecture, JHEP 02 (2016) 128 [arXiv:1504.03566] [INSPIRE].
T.C. Bachlechner, C. Long and L. McAllister, Planckian axions and the weak gravity conjecture, JHEP 01 (2016) 091 [arXiv:1503.07853] [INSPIRE].
G. Shiu, P. Soler and W. Cottrell, Weak gravity conjecture and extremal black holes, Sci. China Phys. Mech. Astron. 62 (2019) 110412 [arXiv:1611.06270] [INSPIRE].
A. Hebecker, P. Mangat, S. Theisen and L.T. Witkowski, Can gravitational instantons really constrain axion inflation?, JHEP 02 (2017) 097 [arXiv:1607.06814] [INSPIRE].
A. Hebecker and P. Soler, The weak gravity conjecture and the axionic black hole paradox, JHEP 09 (2017) 036 [arXiv:1702.06130] [INSPIRE].
T.W. Grimm and D. Van De Heisteeg, Infinite distances and the axion weak gravity conjecture, JHEP 03 (2020) 020 [arXiv:1905.00901] [INSPIRE].
B. Heidenreich, C. Long, L. McAllister, T. Rudelius and J. Stout, Instanton resummation and the weak gravity conjecture, arXiv:1910.14053 [INSPIRE].
T.D. Brennan, F. Carta and C. Vafa, The string landscape, the swampland, and the missing corner, PoS(TASI2017)015 [arXiv:1711.00864] [INSPIRE].
E. Palti, The swampland: introduction and review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Evidence for a sublattice weak gravity conjecture, JHEP 08 (2017) 025 [arXiv:1606.08437] [INSPIRE].
M. Montero, G. Shiu and P. Soler, The weak gravity conjecture in three dimensions, JHEP 10 (2016) 159 [arXiv:1606.08438] [INSPIRE].
L. Aalsma, A. Cole and G. Shiu, Weak gravity conjecture, black hole entropy, and modular invariance, JHEP 08 (2019) 022 [arXiv:1905.06956] [INSPIRE].
S. Andriolo, D. Junghans, T. Noumi and G. Shiu, A tower weak gravity conjecture from infrared consistency, Fortsch. Phys. 66 (2018) 1800020 [arXiv:1802.04287] [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].
C. Cheung and G.N. Remmen, Infrared consistency and the weak gravity conjecture, JHEP 12 (2014) 087 [arXiv:1407.7865] [INSPIRE].
W.-M. Chen, Y.-T. Huang, T. Noumi and C. Wen, Unitarity bounds on charged/neutral state mass ratios, Phys. Rev. D 100 (2019) 025016 [arXiv:1901.11480] [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].
J.H. Schwarz and A. Sen, Duality symmetries of 4D heterotic strings, Phys. Lett. B 312 (1993) 105 [hep-th/9305185] [INSPIRE].
A. Sen, SL(2, ℤ) duality and magnetically charged strings, Int. J. Mod. Phys. A 8 (1993) 5079 [hep-th/9302038] [INSPIRE].
A. Sen, Strong-weak coupling duality in four-dimensional string theory, Int. J. Mod. Phys. A 9 (1994) 3707 [hep-th/9402002] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Order alpha-prime (two loop) equivalence of the string equations of motion and the σ-model Weyl invariance conditions: dependence on the dilaton and the antisymmetric tensor, Nucl. Phys. B 293 (1987) 385 [INSPIRE].
K.A. Meissner and G. Veneziano, Manifestly O(d, d) invariant approach to space-time dependent string vacua, Mod. Phys. Lett. A 6 (1991) 3397 [hep-th/9110004] [INSPIRE].
J.H. Schwarz, Dilaton-axion symmetry, in the proceedings of the International Workshop on String Theory, Quantum Gravity and the Unification of Fundamental Interactions, September 21–26, Rome, Italy (1992), hep-th/9209125 [INSPIRE].
O. Hohm and B. Zwiebach, T-duality constraints on higher derivatives revisited, JHEP 04 (2016) 101 [arXiv:1510.00005] [INSPIRE].
C. Eloy, O. Hohm and H. Samtleben, Duality invariance and higher derivatives, Phys. Rev. D 101 (2020) 126018 [arXiv:2004.13140] [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.W. Gibbons and S.W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
L. Alberte, C. de Rham, S. Jaitly and A.J. Tolley, Positivity bounds and the massless spin-2 pole, arXiv:2007.12667 [INSPIRE].
J. Tokuda, K. Aoki and S. Hirano, Gravitational positivity bounds, arXiv:2007.15009 [INSPIRE].
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Loges, G.J., Noumi, T. & Shiu, G. Duality and supersymmetry constraints on the weak gravity conjecture. J. High Energ. Phys. 2020, 8 (2020). https://doi.org/10.1007/JHEP11(2020)008
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DOI: https://doi.org/10.1007/JHEP11(2020)008