渐近安全重整化群历史的几何化
Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety
摘要：
考虑d维量子Einstein引力中泛函重整化群所隐含的尺度相关有效时空，我们讨论了整个演化历史在具有固定（伪）黎曼结构的（d + 1）维流形上的表示.这个“尺度-时空”带有一个自然的叶理，它的叶子就是在给定分辨率下看到的普通时空。我们提出了高维度量的一种普遍形式，并讨论了它的性质。我们表明，在精确的条件下，这个度量总是里奇平坦的，并承认一个位似的Killing向量场;如果演变的时空是最大对称的，他们的（d + 1）维的代表甚至有一个消失的黎曼张量。非简并的高维度量“几何化”一个给定的RG轨迹与运行的宇宙学常数，我们测试的情况下，渐近安全的单调性要求。
英文摘要：
Considering the scale dependent effective spacetimes implied by the functional renormalization group in d-dimensional Quantum Einstein Gravity, we discuss the representation of entire evolution histories by means of a single, (d + 1)-dimensional manifold furnished with a fixed (pseudo-) Riemannian structure. This "scale-space-time" carries a natural foliation whose leaves are the ordinary spacetimes seen at a given resolution. We propose a universal form of the higher dimensional metric and discuss its properties. We show that, under precise conditions, this metric is always Ricci flat and admits a homothetic Killing vector field; if the evolving spacetimes are maximally symmetric, their (d + 1)-dimensional representative has a vanishing Riemann tensor even. The non-degeneracy of the higher dimensional metric which "geometrizes" a given RG trajectory is linked to a monotonicity requirement for the running of the cosmological constant, which we test in the case of Asymptotic Safety.
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