标题： 量子引力的不动点来自维数正则化 显示英文标题

标题： Fixed Points of Quantum Gravity from Dimensional Regularisation

摘要： 我们研究了量子引力的$\beta$函数，采用了维数正则化方法。 与最小减除法相比，采用了一种非最小重整化方案，该方案能够敏感地处理来自质量项或有量纲耦合的幂律发散。 通过构造，此设置尊重全局和规范对称性，包括微分同胚，并允许系统地扩展到更高的圈阶。 我们在四维量子引力的背景下举例说明了这种方法。 通过计算一环$\beta$函数，我们发现了一个非平凡的不动点。 该不动点显示出两个实临界指数，并且与温伯格的渐近安全性情景相容。 此外，发散结构的基础表明，在紫外区引力实际上变得二维。 我们讨论了我们的结果的意义以及进一步的应用和扩展到更高圈阶的可能性。 显示英文摘要

摘要： We investigate $\beta$-functions of quantum gravity using dimensional regularisation. In contrast to minimal subtraction, a non-minimal renormalisation scheme is employed which is sensitive to power-law divergences from mass terms or dimensionful couplings. By construction, this setup respects global and gauge symmetries, including diffeomorphisms, and allows for systematic extensions to higher loop orders. We exemplify this approach in the context of four-dimensional quantum gravity. By computing one-loop $\beta$-functions, we find a non-trivial fixed point. It shows two real critical exponents and is compatible with Weinberg's asymptotic safety scenario. Moreover, the underlying structure of divergences suggests that gravity becomes, effectively, two-dimensional in the ultraviolet. We discuss the significance of our results as well as further applications and extensions to higher loop orders.