Abstract
In recent literature, it has been argued that a mild form of the Weak Gravity Conjecture (WGC) is satisfied by wide classes of effective field theories in which higher-derivative corrections can be shown to shift the charge-to-mass ratios of extremal black holes to larger values. However, this mild form does not directly constrain low-energy physics because the black holes satisfying the WGC have masses above the cutoff of the effective theory. In this note, we point out that in string theory modular invariance can connect a light superextremal state to heavy superextremal states; the latter collapse into black holes at small string coupling. In the context of heterotic string theory, we show that these states are black holes that have α′-exact charge-to-mass ratios exceeding the classical extremality bound. This suggests that modular invariance of the string partition function can be used to relate the existence of a light superextremal particle to the positive shift in charge-to-mass ratio of extremal black holes.
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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].
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].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP06 (2007) 060 [hep-th/0601001] [INSPIRE].
M. Montero, G. Shiu and P. Soler, The weak gravity conjecture in three dimensions, JHEP10 (2016) 159 [arXiv:1606.08438] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Evidence for a sublattice weak gravity conjecture, JHEP08 (2017) 025 [arXiv:1606.08437] [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].
Y. Kats, L. Motl and M. Padi, Higher-order corrections to mass-charge relation of extremal black holes, JHEP12 (2007) 068 [hep-th/0606100] [INSPIRE].
C. Cheung, J. Liu and G.N. Remmen, Proof of the weak gravity conjecture from black hole entropy, JHEP10 (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, Amplitudes’ positivity, weak gravity conjecture and modified gravity, arXiv:1902.03250 [INSPIRE].
T. Rudelius, Constraints on axion inflation from the weak gravity conjecture, JCAP09 (2015) 020 [arXiv:1503.00795] [INSPIRE].
M. Montero, A.M. Uranga and I. Valenzuela, Transplanckian axions!?, JHEP08 (2015) 032 [arXiv:1503.03886] [INSPIRE].
J. Brown, W. Cottrell, G. Shiu and P. Soler, Fencing in the swampland: quantum gravity constraints on large field inflation, JHEP10 (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, JHEP04 (2016) 017 [arXiv:1504.00659] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Tensionless strings and the weak gravity conjecture, JHEP10 (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].
S.-J. Lee, W. Lerche and T. Weigand, Emergent strings, duality and weak coupling limits for two-form fields, arXiv:1904.06344 [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].
P.A. Cano and A. Ruipérez, Leading higher-derivative corrections to Kerr geometry, JHEP05 (2019) 189 [arXiv:1901.01315] [INSPIRE].
H.S. Reall and J.E. Santos, Higher derivative corrections to Kerr black hole thermodynamics, JHEP04 (2019) 021 [arXiv:1901.11535] [INSPIRE].
A. Schwimmer and N. Seiberg, Comments on the N = 2, N = 3, N = 4 superconformal algebras in two-dimensions, Phys. Lett.B 184 (1987) 191 [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Modular fluxes, elliptic genera and weak gravity conjectures in four dimensions, arXiv:1901.08065 [INSPIRE].
N. Benjamin, E. Dyer, A.L. Fitzpatrick and S. Kachru, Universal bounds on charged states in 2d CFT and 3d gravity, JHEP08 (2016) 041 [arXiv:1603.09745] [INSPIRE].
G.T. Horowitz and J. Polchinski, A correspondence principle for black holes and strings, Phys. Rev.D 55 (1997) 6189 [hep-th/9612146] [INSPIRE].
G. ’t Hooft, The black hole interpretation of string theory, Nucl. Phys.B 335 (1990) 138 [INSPIRE].
L. Susskind, Some speculations about black hole entropy in string theory, hep-th/9309145 [INSPIRE].
A. Sen, Extremal black holes and elementary string states, Mod. Phys. Lett.A 10 (1995) 2081 [hep-th/9504147] [INSPIRE].
G.T. Horowitz and J. Polchinski, Selfgravitating fundamental strings, Phys. Rev.D 57 (1998) 2557 [hep-th/9707170] [INSPIRE].
A. Sen, Black hole entropy function, attractors and precision counting of microstates, Gen. Rel. Grav.40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].
A. Dabholkar, Exact counting of black hole microstates, Phys. Rev. Lett.94 (2005) 241301 [hep-th/0409148] [INSPIRE].
A. Sen, Stretching the horizon of a higher dimensional small black hole, JHEP07 (2005) 073 [hep-th/0505122] [INSPIRE].
P.A. Cano, P.F. Ramírez and A. Ruipérez, The small black hole illusion, arXiv:1808.10449 [INSPIRE].
P.A. Cano et al., Beyond the near-horizon limit: stringy corrections to heterotic black holes, JHEP02 (2019) 192 [arXiv:1808.03651] [INSPIRE].
K. Sfetsos and K. Skenderis, Microscopic derivation of the Bekenstein-Hawking entropy formula for nonextremal black holes, Nucl. Phys.B 517 (1998) 179 [hep-th/9711138] [INSPIRE].
K. Skenderis and M. Taylor, The fuzzball proposal for black holes, Phys. Rept.467 (2008) 117 [arXiv:0804.0552] [INSPIRE].
A. Castro, J.L. Davis, P. Kraus and F. Larsen, String theory effects on five-dimensional black hole physics, Int. J. Mod. Phys.A 23 (2008) 613 [arXiv:0801.1863] [INSPIRE].
J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys.104 (1986) 207 [INSPIRE].
P. Kraus and F. Larsen, Holographic gravitational anomalies, JHEP01 (2006) 022 [hep-th/0508218] [INSPIRE].
P. Kraus and F. Larsen, Microscopic black hole entropy in theories with higher derivatives, JHEP09 (2005) 034 [hep-th/0506176] [INSPIRE].
H. Saida and J. Soda, Statistical entropy of BTZ black hole in higher curvature gravity, Phys. Lett.B 471 (2000) 358 [gr-qc/9909061] [INSPIRE].
E. Halyo, B. Kol, A. Rajaraman and L. Susskind, Counting Schwarzschild and charged black holes, Phys. Lett. B401 (1997) 15 [hep-th/9609075] [INSPIRE].
A. Dabholkar, Microstates of nonsupersymmetric black holes, Phys. Lett.B 402 (1997) 53 [hep-th/9702050] [INSPIRE].
A. Dabholkar, G. Mandal and P. Ramadevi, Nonrenormalization of mass of some nonsupersymmetric string states, Nucl. Phys.B 520 (1998) 117 [hep-th/9705239] [INSPIRE].
A.B. Zamolodchikov, Irreversibility of the flux of the renormalization group in a 2D field theory, JETP Lett.43 (1986) 730 [INSPIRE].
M. Montero, A holographic derivation of the weak gravity conjecture, JHEP03 (2019) 157 [arXiv:1812.03978] [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. Giveon, D. Gorbonos and M. Stern, Fundamental strings and higher derivative corrections to d-dimensional black holes, JHEP02 (2010) 012 [arXiv:0909.5264] [INSPIRE].
M. Montero and G. Shiu, work in progress.
D. Kutasov, F. Larsen and R.G. Leigh, String theory in magnetic monopole backgrounds, Nucl. Phys.B 550 (1999) 183 [hep-th/9812027] [INSPIRE].
N. Arkani-Hamed, Positive geometry of effective field theory, talk given at CERN Winter School on Supergravity, Strings and Gauge Theory, February 4–8, CERN, Geneva, Switzerland (2019).
B. de Wit, S. Katmadas and M. van Zalk, New supersymmetric higher-derivative couplings: full N = 2 superspace does not count!, JHEP01 (2011) 007 [arXiv:1010.2150] [INSPIRE].
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Aalsma, L., Cole, A. & Shiu, G. Weak gravity conjecture, black hole entropy, and modular invariance. J. High Energ. Phys. 2019, 22 (2019). https://doi.org/10.1007/JHEP08(2019)022
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DOI: https://doi.org/10.1007/JHEP08(2019)022