Higher derivative corrections to black brane thermodynamics and the weak gravity conjecture

We study higher derivative corrections to black brane thermodynamics and their implications for the weak gravity conjecture for \(p\)-form gauge fields. In particular we show that higher derivative corrections decrease tension-to-charge ratios of extremal black branes as implied by the weak gravity conjecture, if four-derivative couplings follow scattering positivity bounds. We also demonstrate that entropy corrections in the micro canonical ensemble are positive under the same assumptions. This extends earlier works in the Einstein-Maxwell theory to \(p\)-form gauge fields in general spacetime dimensions.