Non-perturbative aspects of three-dimensional quantum gravity

这个项目将聚焦于三维量子引力的各种非微扰方面。它将涵盖具有正(DS)和负(ADS)宇宙学常数的情况。将使用的工具涉及ADS/CFT，该理论的Chern-Simons公式，以及二维保形场论中的精确方法。对于ADS来说，首要目标是构造一个引力路径积分，并找到一个描述么正量子理论的结果。对于DS来说，一个方面是量化宇宙的Hartle-Hawking波函数，并测试量子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.