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The black hole weak gravity conjecture with multiple charges

Callum R. T. Jones,Brian McPeak

Published 2019 in Journal of High Energy Physics

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 O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document} (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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