Speaker: Nobuyoshi Ohta (Kindai)
Title: Introduction to asymptotic safety
日時：2019年4月16日(火) 16:00から2コマ, 4月17日(水)16:00から2コマ
Abstract: One of the long-standing and important problems in theoretical physics is how to formulate the quantum theory of gravity. In this series of lectures, I will try to explain one of the promising approaches to this problem within the framework of covariant local field theory based on the functional renormalization group, known as asymptotic safety. First, I will explain how the theory of quadratic curvature theory is renormalizable but suffers from the problem of non-unitarity, and the Einstein gravity is nonrenormalizable. Next, I formulate the functional renormalization group equation with effective average action, and explain how to define the quantum gravity using the idea of asymptotic safety and critical surface. This in particular leads us to the notion of nonperturbative renormalizability. I then apply the machinery to the Einstein gravity on the sphere, using the heat kernel expansion. The approach is further extended to f(R) gravity, and discuss if we can decide the dimension of critical surface, or narrow down what kind of theory can be nonperturbatively renormalizable. If time allows, I will discuss the theory with higher curvature theory on arbitrary backgrounds and also the effects of matter.