Quantum Gravity in 2+1 Dimensions

Abstract

General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting becomes an ideal test bed for a wide range of approaches to quantum gravity, from reduced phase phase space quantization to covariant canonical quantization to path integral methods to asymptotic quantization of "edge states." Here I review a variety of classical descriptions of the moduli space of solutions and a broad range of quantizations, with special attention to implications for realistic quantum gravity in four spacetime dimensions.