Non-perturbative aspects of three-dimensional quantum gravity

这个项目将集中于三维量子引力的各种非摄动方面。它将涵盖正（dS）和负（AdS）宇宙常数的情况。将使用的工具与AdS/CFT，理论的chen - simons公式以及二维共形场理论中的精确方法有关。对于AdS，首要目标是构建一个引力路径积分，并找到一个描述酉量子理论的结果。对于dS，一个方面是量化宇宙的Hartle-Hawking波函数，测试量子de Sitter空间的稳定性。

This project will focus on various non-perturbative aspects of three-dimensional quantum gravity. It will cover cases with positive (dS) and negative (AdS) cosmological constant. Tools that will be used are related to AdS/CFT, the Chern-Simons formulation of the theory, and exact methods in two-dimensional conformal field theories. For AdS, the overarching aim is to construct a gravitational path integral and find a result that describes a unitary quantum theory. For dS, one aspect is to quantify the Hartle-Hawking wave function of the universe, and test the stability of quantum de Sitter space.