### Abstract

We consider a two-parameter family of _{2} gauge theories on a lattice discretization $T({\cal M})$ of a three-manifold ${\cal M}$ and its relation to topological field theories. Familiar models such as the spin-gauge model are curves on a parameter space Γ. We show that there is a region Γ _{0} ⊂ Γ where the partition function and the expectation value 〈W _{R}(γ) 〉 of the Wilson loop can be exactly computed. Depending on the point of Γ _{0}, the model behaves as topological or quasi-topological. The partition function is, up to a scaling factor, a topological number of ${\cal M}$. The Wilson loop on the other hand, does not depend on the topology of γ. However, for a subset of Γ _{0}, 〈W _{R}(γ)〉 depends on the size of γ 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.

Original language | English |
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Article number | 1250132 |

Pages (from-to) | 1-22 |

Number of pages | 22 |

Journal | International Journal of Modern Physics A |

Volume | 27 |

Issue number | 23 |

DOIs | |

Publication status | Published - 20 Sep 2012 |

Externally published | Yes |

### Keywords

- gauge theories
- Topological field theories
- Wilson loops

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## Cite this

_{2}lattice gauge theories.

*International Journal of Modern Physics A*,

*27*(23), 1-22. [1250132]. https://doi.org/10.1142/S0217751X12501321