2 + 1 dimensional gravity as an exactly soluble system
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 YangMills theory with purely the ChernSimons 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 threedimensional geometry.
 Publication:

Nuclear Physics B
 Pub Date:
 December 1988
 DOI:
 10.1016/05503213(88)901435
 Bibcode:
 1988NuPhB.311...46W