Title: Positivity bounds in the presence of gravity
Positivity bounds for theories with massless spin-2 fields would have deep implications for UV physics and the Weak Gravity Conjecture. However, the presence of a singularity in the t-channel of the scattering amplitudes precludes the application of standard positivity bounds. I will discuss the recent progress in understanding the implications of the positivity bounds when applied to the scattering amplitudes with the t-channel pole subtracted. I will show how for simple renormalizable field theories coupled to gravity this leads to constraints on the low-energy coupling constants in a way which is incompatible with their actual values, implying new physics at a scale parametrically smaller than expected. I will pay special attention to the case of QED minimally coupled to gravity. I will emphasize how this is sharply contrasted with previous treatments which focus on the application of positivity bounds to the low energy gravitational Euler-Heisenberg effective theory only.