Functional Renormalization Group Methods in Quantum Gravity

理论高能物理学的主要挑战之一是建立一个在所有距离尺度上都有效的引力基本理论。虽然这样的描述尚不为人所知，但它有望为诸如宇宙常数的微小值或暗物质的起源等核心问题提供答案。这一提议将引领对量子引力的一个有希望的候选理论的探索，即温伯格的渐近安全场景。这里的关键思想是，引力在非摄动水平上是一个一致的、可预测的量子理论。分析研究这种情况的主要工具是泛函重整化群方程，它为理论的非摄动性质提供了一个重要的窗口。到目前为止，这些研究已经为渐近安全性提供了大量证据，但尚未得出结论。因此，我们的建议将开发研究纯重力、重力物质和超重力理论的非微扰重整化群流的新技术。这些将用于实施渐近安全性的几个酸测试，并研究其对早期宇宙，黑洞，宇宙学和超对称物理学的现象学结果。此外，将迄今为止不相关的量子引力候选理论联系起来，我们的工作将促进对该研究领域中几个开放概念点的理解。

One of the major challenges in theoretical high energy physics is the construction of a fundamental theory of gravity valid at all distance scales. While such a description is yet unknown, it is expected to provide answers to central questions such as the tiny value of the cosmological constant or the origin of dark matter. This proposal will spearhead the exploration of a promising candidate theory for Quantum Gravity, Weinberg’s asymptotic safety scenario. Here the key idea is that gravity is a consistent and predictive quantum theory at the nonperturbative level. The primary tools for investigating this scenario analytically are functional renormalization group equations, which provide an important window on the non-perturbative properties of the theory. So far these have yielded substantial evidence for asymptotic safety without yet being conclusive. Thus our proposal will develop new techniques for studying the non-perturbative renormalization group flow of pure gravity, gravity-matter, and supergravity theories. These will be used to implement several acid tests for asymptotic safety and study its phenomenological consequences for the physics of the early universe, black holes, cosmology and supersymmetry. Moreover, connecting hitherto unrelated candidate theories of Quantum Gravity, our work will boost the understanding of several open conceptual points in this research area.