Abstract

In this talk I will discuss positivity bounds on the effective field theory (EFT) of photons, derived from dispersion relations and the generalised optical theorem. In general, basic assumptions on the high-energy UV completion, such as unitarity and partial wave decomposition, imply bounds on the space of the Wilson coefficients parametrising the low-energy EFT . We develop a method that allows us to bound Wilson coefficients appearing in amplitudes of all possible polarisations, not just the forward amplitudes. In the absence of dynamical gravity, such bounds imply a set of inequalities known as the Black Hole Weak Gravity Conjecture (WGC). However, in the presence of dynamical gravity, we find that the dispersion relation argument alone cannot rule out a small violations of the Black Hole WGC , and we determine the maximum allowed size of such violations.