On three-dimensional topological field theories constructed from $D^{\omega }(G)$ for finite group

Abstract

We investigate the 3d lattice topological field theories defined by Chung, Fukuma and Shapere. We concentrate on the model defined by taking a deformation $\text{D}G$ of the quantum double of a finite commutative group $G$ as the underlying Hopf algebra. It is suggested that Chung-Fukuma-Shapere partition function is related to that of Dijkgraaf-Witten by $\text{zcfs}=|\text{zdw}{|}^2$ when $G={\mathbb{Z}}_{2N+1}$. For $G={\mathbb{Z}}_{2N}$, such a relation does not hold.

Comments: 13 pages, 3 PS figures included