Duality and the Weak Gravity Conjecture

In the Einstein-Maxwell theory the Weak Gravity Conjecture follows exactly from the positivity bounds on the scattering amplitudes imposed by locality, Lorentz invariance and unitarity of the S-matrix. However, this is in general not true anymore for theories beyond the pure Einstein-Maxwell. An interesting possibility to restore this equivalence is to require the theory to preserve electromagnetic duality. In this work we explore this idea in the context of the axion-dilaton-Maxwell-Einstein theory. First, we study the duality group of this theory and we analytically derive its duality-preserving, 4-derivatives extension. Then, we determine the subset of values of the higher-order coefficients that realizes the Weak Gravity Conjecture by studying the corrections to the charge-to-mass ratio of a black hole solution of such extended theory. Finally, we compare such constraints with the positivity bounds on the scattering amplitudes in order to check the claimed equivalence between the two requirements.