Quasi-topological quantum field theories and 2 lattice gauge theories

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

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Article number1250132
Pages (from-to)1-22
Number of pages22
JournalInternational Journal of Modern Physics A
Volume27
Issue number23
DOIs
Publication statusPublished - 20 Sep 2012
Externally publishedYes

Keywords

  • gauge theories
  • Topological field theories
  • Wilson loops

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