论文标题
纯量子重力中的重新归一化组方程和复发极关系
Renormalization group equations and the recurrence pole relations in pure quantum gravity
论文作者
论文摘要
在尺寸正则化的框架中，我们提出了重新归一化组方程的概括，如果涉及度量和高阶Riemann曲率耦合的扰动量子重力。考虑了零宇宙常数的情况。求解重新归一化组（RG）方程，我们计算了相应的beta功能并得出复发关系，在牛顿常数中以任何顺序有效，将较高的极项$ 1/（d-4）^n $与单极$ 1/（d-4）相关联。使用复发关系，我们找到了出现在2、3和4循环中的较高极点的确切形式，并且我们对任何环中高极反向处理的一般结构进行了某些陈述。我们表明，裸露的重力作用中隐藏的紫外线发散项的完整集可以（按牛顿常数中的任何顺序）保持一致，其中包括riemann张量中的较高顺序的术语，前提是指标和较高的曲率耦合是根据RG方程重新归一化的。
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.
