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We derive new bounds on higher-dimension operator coefficients infour-dimensional Einstein-Maxwell theory. Positivity of classically-generatedcorrections to the Wald entropy of thermodynamically stable, rotating dyonicblack holes implies a multiparameter family of field basis invariantinequalities that exhibit electromagnetic duality and are satisfied by examplesfrom field and string theory. These bounds imply that effective operatorsmodify the extremality condition of large black holes so as to permit theirdecay to smaller ones, thus satisfying the weak gravity conjecture.

Entropy Bounds on Effective Field Theory from Rotating Dyonic Black Holes