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 ${\mathrm{\Lambda }}_{\mathrm{new}}\sim (em{M}_{\mathrm{Pl}}{)}^{1/2}$, 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 emphasize 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 is not in conflict with standard UV completions, including weakly coupled ones.

中文翻译：

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QED 积极性界限

我们将积极性界限直接应用于 $你(1)$带电标量和带电费米子的规范理论，即 QED，与重力的耦合最小。假设无质量$吨$-通道极点可能会被丢弃，我们表明除非在参数低尺度引入新物理，否则会违反改进的正边界 ${\mathrm{\Lambda }}_{\mathrm{新的}}～(\mathrm{电子}米{米}_{\mathrm{PL}}{)}^{1/2}$，与标量场理论的类似结果一致，远低于弱引力猜想所暗示的尺度。这与之前的处理形成鲜明对比，这些处理专注于将正界应用于低能引力欧拉-海森堡有效理论。我们强调低截止值是在极点可能被丢弃的假设下应用正边界的结果。我们推测另一种解决方案，即允许与解耦限制一致的少量负值，并且与标准 UV 完成（包括弱耦合完成）不冲突。