1206.2158 (Miguel J. B. Ferreira et al.)

Quasi-Topological Quantum Field Theories and $Z_2$ Lattice Gauge
Theories    [PDF]

Miguel J. B. Ferreira, Victor A. Pereira, P. Teotonio-Sobrinho

We consider a two parameter family of $Z_2$ gauge theories on a lattice discretization $T(M)$ of a 3-manifold $M$ and its relation to topological field theories. Familiar models such as the spin-gauge model are curves on a parameter space $\Gamma$. We show that there is a region $\Gamma_0$ of $\Gamma$ where the partition function and the expectation value $$ of the Wilson loop for a curve $\gamma$ can be exactly computed. Depending on the point of $\Gamma_0$, the model behaves as topological or quasi-topological. The partition function is, up to a scaling factor, a topological number of $M$. The Wilson loop on the other hand, does not depend on the topology of $\gamma$. However, for a subset of $\Gamma_0$, $$ depends on the size of $\gamma$ and follows a discrete version of an area law. At the zero temperature limit, the spin-gauge model approaches the topological and the quasi-topological regions depending on the sign of the coupling constant.

View original: http://arxiv.org/abs/1206.2158