标题： 规范和截断函数在量子引力紫外不动点中的依赖性 显示英文标题

标题： Gauge and Cutoff Function Dependence of the Ultraviolet Fixed Point in Quantum Gravity

摘要： 纯量子引力的精确重整化群方程在时空维度$d=4$中对于任意规范参数进行了推导。 该方程由有效平均作用量的非线性泛函微分方程给出。 有效平均作用量的作用泛函被近似为与爱因斯坦-希尔伯特作用量相同的功能空间。 从这个近似中，得到了无量纲牛顿常数和宇宙学常数的$\beta$-函数，且是非微扰地得出的。 这些函数用于分析无量纲牛顿常数的相结构和紫外非高斯固定点。 这个固定点强烈依赖于规范参数和截断函数。 然而，除了某些规范之外，这个固定点不存在这些不确定性。 因此，纯量子引力在$d=4$中可能是一个渐近安全理论，并且是非微扰可重整化的。 显示英文摘要

摘要： The exact renormalization group equation for pure quantum gravity is derived for an arbitrary gauge parameter in the space-time dimension $d=4$. This equation is given by a non-linear functional differential equation for the effective average action. An action functional of the effective average action is approximated by the same functional space of the Einstein-Hilbert action. From this approximation, $\beta$-functions for the dimensionless Newton constant and cosmological constant are derived non-perturbatively. These are used for an analysis of the phase structure and the ultraviolet non-Gaussian fixed point of the dimensionless Newton constant. This fixed point strongly depends on the gauge parameter and the cutoff function. However, this fixed point exists without these ambiguities, except for some gauges. Hence, it is possible that pure quantum gravity in $d=4$ is an asymptotically safe theory and non-perturbatively renormalizable.