# 2 + 1 dimensional gravity as an exactly soluble system

- Authors
- Journal
- Nuclear Physics B 0550-3213
- Publisher
- Elsevier
- Publication Date
- Volume
- 311
- Issue
- 1
- Identifiers
- DOI: 10.1016/0550-3213(88)90143-5
- Disciplines

## Abstract

Abstract By disentangling the hamiltonian constraint equations, 2 + 1 dimensional gravity (with or without a cosmological constant) is shown to be exactly soluble at the classical and quantum levels. Indeed, it is closely related to Yang-Mills theory with purely the Chern-Simons action, which recently has turned out to define a soluble quantum field theory. 2 + 1 dimensional gravity has a straightforward renormalized perturbation expansion, with vanishing beta function. 2 + 1 dimensional quantum gravity may provide a testing ground for understanding the role of classical singularities in quantum mechanics, may be related to the discrete series of Virasoro representations in 1 + 1 dimensions, and may be a useful tool in studying three-dimensional geometry.

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