QED positivity bounds

TL;DR

Applying positivity bounds to QED with gravity suggests new physics must appear at a low scale unless negativity is allowed, challenging previous assumptions and the weak gravity conjecture.

Contribution

This work applies improved positivity bounds directly to QED coupled with gravity, revealing a low cutoff scale and proposing an alternative resolution involving small negativity.

Findings

Positivity bounds imply a low new physics scale in QED with gravity.

Discarding the massless t-channel pole leads to bounds violation without new physics.

Allowing small negativity resolves the bounds without conflicting with UV completions.

Abstract

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. We emphasise that the low-cutoff is a consequence of applying the positivity bounds under the assumption that the pole may be discarded. We conjecture an alternative resolution that a small amount of negativity, consistent with decoupling limits, is allowed and not in conflict with standard UV completions, including weakly coupled ones.