CFT constraints on the weak gravity conjecture
- 1Damghan University
- 2Khazar University
- 3Eastern Mediterranean University
Abstract
The Weak Gravity Conjecture (WGC) is a swampland criterion of long standing: any consistent theory of quantum gravity must contain a charged particle whose charge-to-mass ratio exceeds that of an extremal black hole, so that gravity remains the weakest force. Quasinormal modes of a near-extremal black hole are poles of a retarded Green’s function of the conformal quantum mechanics living on the near-horizon AdS 2 2 throat, and their damping rate is bounded from below by the Hawking temperature. We show that this pairing fixes the WGC bound in closed form. Only two numbers survive from the bulk geometry, the AdS 2 2 radius L2 L 2 and the electric-field parameter ed e d of the throat, and the conjecture reads q/m ≥ L2/ed q / m ≥ L 2 / e d . We evaluate this quantity for two backgrounds that fall outside the Reissner–Nordström idealisation in different ways: static spherically symmetric black holes in dRGT massive gravity, and electrically charged black holes in Einstein–ModMax non-linear electrodynamics, the latter taken throughout in its purely electric sector, where the pseudoscalar invariant G vanishes. For dRGT the massive-gravity couplings do not drop out. The bound becomes q/m ≥ √(D/A) q / m ≥ D / A with A = 1+ζ +Λ r+2 + 2γ g r+ A = 1 + ζ + Λ r + 2 + 2 γ g r + and D = 1+ζ +2Λ r+2+3γ g r+ D = 1 + ζ + 2 Λ r + 2 + 3 γ g r + , so the deviation from the Reissner–Nordström value is second order in the graviton mass and is positive whenever Λ r+ + γ g > 0 Λ r + + γ g > 0 . For Einstein–ModMax the duality parameter enters through the charge normalisation of the non-linear displacement field, giving q/m ≥ eγ /2 q / m ≥ e γ / 2 , which coincides identically with the charge-to-mass ratio Qext/Mext Q ext / M ext of the extremal solution. That coincidence is a sharp check on the whole construction. We then relax exact extremality, minimal coupling and the two-derivative truncation, and follow how each relaxation feeds back into L2 L 2 and ed e d . Every closed form is cross-checked twice, once symbolically and once against a Runge–Kutta integration of the full radial Klein–Gordon equation that extracts the conformal weight from the horizon exponents without using the throat approximation; the two agree to eleven digits.
Related
- Wormhole fragmentation and the axion Weak Gravity Conjecture
- Instanton Interactions and the Axion Weak Gravity Conjecture
- Freezing Swampland: A Krylov Complexity Diagnostic for the Weak Gravity Conjecture
- Moduli space curvature and the weak gravity conjecture
- Pair creation in weak gravity and gauge backgrounds: spinning fields and binary stars
BibTeX
@article{gashti2026constraints,
title = {{CFT constraints on the weak gravity conjecture}},
author = {Saeed Noori Gashti and Behnam Pourhassan and İzzet Sakallı},
journal = {The European Physical Journal C},
year = {2026},
month = oct,
doi = {10.1140/epjc/s10052-026-16427-z},
url = {https://link.springer.com/10.1140/epjc/s10052-026-16427-z},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - CFT constraints on the weak gravity conjecture
AU - Saeed Noori Gashti
AU - Behnam Pourhassan
AU - İzzet Sakallı
PY - 2026
DA - 2026/10/05
JO - The European Physical Journal C
DO - 10.1140/epjc/s10052-026-16427-z
UR - https://link.springer.com/10.1140/epjc/s10052-026-16427-z
AB - The Weak Gravity Conjecture (WGC) is a swampland criterion of long standing: any consistent theory of quantum gravity must contain a charged particle whose charge-to-mass ratio exceeds that of an extremal black hole, so that gravity remains the weakest force. Quasinormal modes of a near-extremal black hole are poles of a retarded Green’s function of the conformal quantum mechanics living on the near-horizon AdS _2 2 throat, and their damping rate is bounded from below by the Hawking temperature. We show that this pairing fixes the WGC bound in closed form. Only two numbers survive from the bulk geometry, the AdS _2 2 radius L_2 L 2 and the electric-field parameter e_d e d of the throat, and the conjecture reads q/m ≥ L_2/e_d q / m ≥ L 2 / e d . We evaluate this quantity for two backgrounds that fall outside the Reissner–Nordström idealisation in different ways: static spherically symmetric black holes in dRGT massive gravity, and electrically charged black holes in Einstein–ModMax non-linear electrodynamics, the latter taken throughout in its purely electric sector, where the pseudoscalar invariant G vanishes. For dRGT the massive-gravity couplings do not drop out. The bound becomes q/m ≥ √(D/A) q / m ≥ D / A with A = 1+ζ +Λ r_+^2 + 2γ _g r_+ A = 1 + ζ + Λ r + 2 + 2 γ g r + and D = 1+ζ +2Λ r_+^2+3γ _g r_+ D = 1 + ζ + 2 Λ r + 2 + 3 γ g r + , so the deviation from the Reissner–Nordström value is second order in the graviton mass and is positive whenever Λ r_+ + γ _g > 0 Λ r + + γ g > 0 . For Einstein–ModMax the duality parameter enters through the charge normalisation of the non-linear displacement field, giving q/m ≥ e^γ /2 q / m ≥ e γ / 2 , which coincides identically with the charge-to-mass ratio Q_ext/M_ext Q ext / M ext of the extremal solution. That coincidence is a sharp check on the whole construction. We then relax exact extremality, minimal coupling and the two-derivative truncation, and follow how each relaxation feeds back into L_2 L 2 and e_d e d . Every closed form is cross-checked twice, once symbolically and once against a Runge–Kutta integration of the full radial Klein–Gordon equation that extracts the conformal weight from the horizon exponents without using the throat approximation; the two agree to eleven digits.
SN - 1434-6044
SN - 1434-6052
ER -