QED positivity bounds

Understand

We apply positivity bounds directly to a $U(1)$ gauge theory with charged scalars and charged fermions, i.e.

• QED, minimally coupled to gravity.
• Assuming that the massless $t$-channel pole may be discarded, we show that the improved positivity bounds are violated unless new physics is introduced at the parametrically low scale $\Lambda_{\rm new} \sim (e m M_{\rm pl})^{1/2}$, consistent with similar results for scalar field theories, far lower than the scale implied by the weak gravity conjecture.
• 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.