This paper is part of a series of papers exploring the renormalization of field theories coupled to gravity using the effective field theory framework. In previous works, we studied the universality of the electric charge and the two-loops beta function in the Einstein-QED system. Now, we use this framework to study the non-Abelian gauge theory with fermions coupled to gravity. We show that even though some of the counterterms are dependent on the gravitational coupling, the renormalized coupling constant, and therefore the beta function, do not receive any gravitational correction at one-loop order. Also, we explicitly show that, at this order, the Slavnov-Taylor identities are respected. Finally, we end the paper by putting into perspective the results of the present and the past papers.

中文翻译：

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对非阿贝尔规范理论的引力修正

本文是使用有效场论框架探索与重力耦合的场论重整化系列论文的一部分。在之前的工作中，我们研究了 Einstein-QED 系统中电荷的普遍性和双环 beta 函数。现在，我们使用这个框架来研究费米子与引力耦合的非阿贝尔规范理论。我们表明，即使某些反项依赖于引力耦合，重整化的耦合常数以及因此的 beta 函数也不会在单环阶上接受任何引力校正。此外，我们明确表明，按照这个顺序，Slavnov-Taylor 身份得到尊重。最后，我们通过透视当前和过去论文的结果来结束本文。