In the framework of dimensional regularization, we propose a generalization of the renormalization group equations in the case of the perturbative quantum gravity that involves renormalization of the metric and of the higher order Riemann curvature couplings. The case of zero cosmological constant is considered. Solving the renormalization group (RG) equations we compute the respective beta functions and derive the recurrence relations, valid at any order in the Newton constant, that relate the higher pole terms $1/{(d-4)}^n$ to a single pole $1/(d-4)$ in the quantum effective action. Using the recurrence relations we find the exact form for the higher pole counter-terms that appear in 2, 3 and 4 loops and we make certain statements about the general structure of the higher pole counter-terms in any loop. We show that the complete set of the UV divergent terms can be consistently (at any order in the Newton constant) hidden in the bare gravitational action, that includes the terms of higher order in the Riemann tensor, provided the metric and the higher curvature couplings are renormalized according to the RG equations.

在尺寸正则化的框架中，我们提出了在微扰的量子引力的情况下，对度量和高阶黎曼曲率耦合进行归一化的归一化群方程的推广。考虑宇宙常数为零的情况。求解重归一化组（RG）方程，我们计算相应的beta函数，并得出与牛顿常数相关的，在牛顿常数中以任意顺序有效的递归关系。$\mathrm{1个}/{（d-4）}^{ñ}$ 到单极 $\mathrm{1个}/（d-4）$在量子有效的作用。使用递归关系，我们可以找到出现在2、3和4循环中的较高极反术语的确切形式，并对任何循环中较高极反术语的一般结构做出某些陈述。我们表明，紫外线散度项的完整集合可以一致地隐藏（在牛顿常数中的任何顺序）在裸引力作用下，其中包括度量和较高曲率耦合的黎曼张量中的高阶项。根据RG方程重新归一化。