In this work, we use the framework of effective field theory to couple Einstein’s gravity to quantum electrodynamics (QED) and determine the gravitational corrections to the two-loop beta function of the electric charge in arbitrary electrodynamics (Lorentz-like) and arbitrary (de Donder–like) gravitational gauges. Our results indicate that gravitational corrections do not alter the running behavior of the electric charge; on the contrary, we observe that it gives a positive contribution to the beta function, making the electric charge grow even faster.

中文翻译：

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量子电动力学中双环β函数的引力修正

在这项工作中，我们使用有效场论的框架将爱因斯坦的引力与量子电动力学 (QED) 耦合，并确定对任意电动力学 (Lorentz-like) 和任意 (de类似唐德的）引力计。我们的结果表明重力修正不会改变电荷的运行行为；相反，我们观察到它对 beta 函数有积极的贡献，使电荷增长得更快。