Three-dimensional gravity from the Turaev-Viro invariant.

We study the {ital q}-deformed su(2) spin network as a three-dimensional quantum gravity model. We show that in the semiclassical continuum limit the Turaev-Viro invariant obtained recently defines a naturally regularized path integral {ital a} {ital la} Ponzano and Regge, in which a contribution from the cosmological term is effectively included. The regularization-dependent cosmological constant is found to be 4{pi}{sup 2}/{ital k}{sup 2}+{ital O}({ital k}{sup {minus}4}), where {ital q}{sup 2{ital k}}=1. We also discuss the relation to the Euclidean Chern-Simons-Witten gravity in three dimensions.