QED positivity bounds

We apply positivity bounds directly to a $U(1)$ gauge theory with charged scalars and fermions, i.e., QED, minimally coupled gravity. Assuming that the massless $t$-channel pole may be discarded, we show improved are violated unless new physics is introduced at parametrically low scale ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{new}}\ensuremath{\sim}(em{M}_{\mathrm{Pl}}{)}^{1/2}$, consistent similar results for scalar field theories, far lower than implied by weak gravity conjecture. This sharply contrasted previous treatments which focus on application of energy gravitational Euler-Heisenberg effective only. emphasize cutoff consequence applying under assumption discarded. conjecture an alternative resolution small amount negativity, decoupling limits, allowed not in conflict standard UV completions, including weakly ones.