标题： 在壳微扰理论中的渐近安全性 显示英文标题

标题： Asymptotic Safety within on-shell perturbation theory

摘要： 我们使用维度正则化中的新颖减去方案来研究爱因斯坦引力的重整化。 牛顿常数的一环β函数从偶数维中的极点获得，并可以映射到使用适当时间截断得到的β函数。 通过场重定义来消除重整化群方程中的非壳上贡献。 为了检查我们近似的自洽性，我们使用了度规涨落的一般参数化。 在导数展开和牛顿常数展开的截断中，我们表明参数化依赖性可以逐阶消除。 在标量曲率的所有阶次上，得到了一个与参数化无关的牛顿常数的全阶β函数。 β函数在Reuter固定点处为零，临界指数与非微扰计算结果高度一致。 最后，我们将临界指数与通过因果动态三角剖分（CDT）计算的对应值进行了比较。 显示英文摘要

摘要： We investigate the renormalisation of Einstein gravity using a novel subtraction scheme in dimensional regularisation. The one-loop beta function for Newton's constant receives contributions from poles in even dimensions and can be mapped to the beta function obtained using a proper-time cutoff. Field redefinitions are used to remove off-shell contributions to the renormalisation group equations. To check the consistency of our approximations we use a general parametrisation of the metric fluctuation. Within truncations of the derivative expansion and the expansion in Newton's constant, we show that the parametrisation dependence can be removed order by order. Going to all orders in the scalar curvature an all-order beta function for Newton's constant is obtained that is independent of the parameterisation. The beta function vanishes at the Reuter fixed point and the critical exponent is in good agreement with non-perturbative calculations. Finally, we compare the critical exponent to the counterpart computed via Causal Dynamical Triangulations (CDT).