I review the field-theoretic renomalization group approach to quantumgravity, built around the existence of a non-trivial ultraviolet fixed point infour dimensions. I discuss the implications of such a fixed point, found inthree largely unrelated non-perturbative approaches, and how it relates to thevacuum state of quantum gravity, and specifically to the running of $G$. Onedistinctive feature of the new fixed point is the emergence of a secondgenuinely non-perturbative scale, analogous to the scaling violation parameterin non-abelian gauge theories. I argue that it is natural to identify such ascale with the small observed cosmological constant, which in quantum gravitycan arise as a non-perturbative vacuum condensate. (Plenary Talk, 12-th Marcel Grossmann Conference on Recent Developments inGeneral Relativity, Astrophysics and Relativistic Field Theories, UNESCO Paris,July 12-18, 2009).
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机译：我回顾了量子重力的场论理论重整化组方法，该方法围绕四个维度上的非平凡紫外线固定点的存在而建立。我讨论了这样一个固定点的含义，发现了三种在很大程度上无关的非扰动方法，以及它与量子引力的真空状态，特别是与$ G $的运行有关。新的固定点的一个显着特征是出现了第二个非扰动标度，类似于非阿贝尔规范理论中的标度违规参数。我认为很自然地用一个小的观测到的宇宙常数来确定这样一个尺度，宇宙常数在量子引力中可以作为无扰动的真空冷凝物出现。 （全体演讲，第12届马塞尔·格罗斯曼关于广义相对论，天体物理学和相对论领域理论的最新发展会议，联合国教科文组织巴黎，2009年7月12日至18日）。
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