On the Renormalization Group Flow of Gravity
On the Renormalization Group Flow of Gravity
复制标题
关于重力重正化群流
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
F. Saueressig
中科院分区：
文献类型：
--
作者：
P. F. Machado;F. Saueressig
把引力理解为一个基本理论意味着理解它在我们跨越不同长度尺度时的行为。在本论文中，我们通过研究引力重整化群流来研究这种尺度依赖行为。我们研究的一个中心焦点是渐近安全方案，它假定存在一个引力重整化群的非平凡不动点，控制着理论在紫外线下的行为，并为它提供了一个预测性和明确定义的高能极限。我们的主要工具是连续威尔逊重整化群技术，泛函重整化群方程。在这个框架内的计算依赖于截断近似，从而将完整的重整化群流投影到理论耦合的子空间上。由此得到的结果的可靠性进行了评估，通过验证其稳定性下的截断子空间的逐步扩展。最简单的非平凡引力截断是爱因斯坦-希尔伯特截断，其中首次发现了支持渐近安全场景的非平凡引力不动点的证据。关键的问题是，这个不动点在截断子空间进一步扩大的情况下是否仍然存在。在这篇论文中，我们通过以下三个互补的策略来解决这个问题。首先，在第三章中，我们研究了限制在共形扇区内的引力重整化群流。这种简化使我们能够考虑包含由于技术原因而难以处理的项的截断，从而获得这些项对完整理论行为的影响的大致情况。我们在第4章和第5章中采用的第二种策略，回到完全引力的情况，是构造一个泛函重整化群方程，使我们能够研究曲率标量的任意函数f（R）所张成的一般截断，从而研究完全重整化群流空间的大扇区。最后，在第6章中，我们在我们的截断项中包括了从微扰量子化的观点来看特别有问题的截断项。首先，我们超越了f（R）的情况，在截断中明确地包含了四阶导数张量算子，然后在截断中加入了一个最小耦合的无质量标量场。值得注意的是，在所有这些扩展中，都发现了一个非平凡的紫外不动点，这些研究产生的相干图像为渐近安全场景提供了重要的证据，并表明量子化引力在任意小尺度下仍然具有预测性。
Understanding gravity as a fundamental theory implies understanding its behavior as we move across different length scales. In the present thesis, we have investigated this scale-dependent behavior by studying the renormalization group flow of gravity. A central focus of our investigations was the asymptotic safety scenario, which posits the existence of a non-trivial fixed point of the gravitational renormalization group controlling the behavior of the theory in the ultraviolet and providing it with a predictive and well-defined high-energy limit. Our main tool was a continuous Wilsonian renormalization group technique, the functional renormalization group equation. Computations within this framework rely on truncation approximations, whereby the full renormalization group flow is projected onto a subspace of the couplings of the theory. The reliability of the results thus obtained is assessed by verifying their stability under the gradual extension of the truncation subspace. The simplest, non-trivial gravity truncation one may consider is the Einstein-Hilbert truncation, in which evidence was first found for a non-trivial fixed point of gravity in support of the asymptotic safety scenario. The crucial question is then whether or not this fixed point persists under further enlargement of the truncation subspaces. In this thesis, we have tackled this question by following three complementary strategies. First, in Chapter 3, we investigated the renormalization group flow of gravity restricted to the conformal sector. This simplification allowed us to consider truncations containing terms which would be otherwise intractable for technical reasons, and thus obtain a rough picture of the effect of those terms on the behavior of the complete theory. A second strategy, which we followed in Chapters 4 and 5, returning to the case of full gravity, was to construct a functional renormalization group equation that allowed us to study general truncations spanned by arbitrary functions $f(R)$ of the curvature scalar, and hence investigate large sectors of the full renormalization group flow space. Lastly, in Chapter 6, we included in our truncation terms which are known to be particularly problematic from the point of view of perturbative quantization. First, we moved beyond the $f(R)$-case by explicitly including four-derivative tensorial operators in our truncation, and then added a minimally coupled, massless scalar field to our truncation. Remarkably, in all of these extensions a non-trivial ultraviolet fixed point was found. The coherent picture that arises from these studies provides significant evidence in favor of the asymptotic safety scenario, and suggests that quantized gravity remains predictive at arbitrarily small scales.