Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe

TL;DR

This paper reviews the progress in quantizing (2+1)-dimensional vacuum gravity within a closed universe, highlighting the simplifications and remaining conceptual challenges in quantum gravity.

Contribution

It provides a comprehensive summary of methods and results in the quantization of 2+1 dimensional gravity with a closed universe topology.

Findings

Quantization approaches for 2+1D gravity are summarized.

Conceptual problems of quantum gravity persist despite simplifications.

The review covers a large body of existing work.

Abstract

In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2+1)-dimensional vacuum gravity in the setting of a spatially closed universe.