Quantum Gravity in 2+1 Dimensions

TL;DR

This paper reviews classical and quantum descriptions of gravity in 2+1 dimensions, highlighting its simplicity as a test bed for quantum gravity approaches and discussing implications for 4D theories.

Contribution

It provides a comprehensive overview of classical moduli space and various quantization methods in 2+1D gravity, connecting insights to four-dimensional quantum gravity.

Findings

Classical solutions have constant curvature and are well-characterized.

Multiple quantization approaches are applicable to 2+1D gravity.

Insights from 2+1D models inform quantum gravity in 4D.

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.