Abstract
We study the effect of higher-derivative corrections on asymptotically flat, four-dimensional, dyonic black holes in low-energy models of gravity coupled to N U(1) gauge fields. For large extremal black holes, the leading \( \mathcal{O} \) (1/Q2) correction to the extremality bound is calculated from the most general low-energy effective action containing operators with up to four derivatives. Motivated by the multi-charge generalization of the Weak Gravity Conjecture, we analyze the necessary kinematic conditions for an asymptotically large extremal black hole to decay into a multi-particle state of extremal black holes. In the large black hole regime, we show that the convex hull condition degenerates to the requirement that a certain quartic form constructed from the Wilson coefficients of the four- derivative effective operators, is everywhere positive. Using on-shell unitarity methods, we show that higher-derivative operators are renormalized at one-loop only if they generate local, on-shell matrix elements that are invariant tensors of the electromagnetic duality group U(N). The one-loop logarithmic running of the four-derivative Wilson coefficients is calculated and shown to imply the positivity of the extremality form at some finite value of Q2. This result generalizes an argument recently given by Charles [1], and shows that under the given assumptions the multi-charge Weak Gravity Conjecture is not a Swampland criterion.
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Jones, C.R., McPeak, B. The black hole weak gravity conjecture with multiple charges. J. High Energ. Phys. 2020, 140 (2020). https://doi.org/10.1007/JHEP06(2020)140
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DOI: https://doi.org/10.1007/JHEP06(2020)140