标题： 如何理解六阶导数量子引力中的β函数结构？ 显示英文标题

标题： How to understand the Structure of Beta Functions in Six-derivative Quantum Gravity?

摘要： 我们广泛地阐述了高阶导数引力的研究，特别是强调在定义中包含六个导数的理论所具有的新量子特性。 接下来，我们讨论了在最小六阶导数量子引力中，针对一般协变项前的三个耦合常数（Weyl张量平方、里奇标量平方和高斯-博内标量）在全量子水平上之前获得的精确β函数的数学结构，这些项具有四个导数，在$d=4$维时空情况下。 在这里起基础作用的是原始作用量中Weyl张量项前的耦合常数与里奇标量项前的耦合常数的比值$x$。 我们将$x$的多项式依赖关系与模型中增强共形对称性的有无以及可重整化性联系起来，在四阶导数和六阶导数理论的情况下分别正式地为$x\to+\infty$。 显示英文摘要

摘要： We extensively motivate the studies of higher-derivative gravities, and in particular we emphasize which new quantum features theories with six derivatives in their definitions possess. Next, we discuss the mathematical structure of the exact on the full quantum level beta functions obtained previously for three couplings in front of generally covariant terms with four derivatives (Weyl tensor squared, Ricci scalar squared and the Gauss-Bonnet scalar) in minimal six-derivative quantum gravity in $d=4$ spacetime dimensions. The fundamental role here is played by the ratio $x$ of the coupling in front of the term with Weyl tensors to the coupling in front of the term with Ricci scalars in the original action. We draw a relation between the polynomial dependence on $x$ and the absence/presence of enhanced conformal symmetry and renormalizability in the models where formally $x\to+\infty$ in the case of four- and six-derivative theories respectively.