The black hole weak gravity conjecture with multiple charges
Callum R.T. Jones, Brian McPeak
Abstract
A bstract 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 $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> (1/ Q 2 ) 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 Q 2 . 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.