Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-03-02
Int.J.Mod.Phys. A13 (1998) 3667-3690
Physics
High Energy Physics
High Energy Physics - Theory
23 pages, 16 figures, uses psbox.tex
Scientific paper
10.1142/S0217751X98001724
We study a class of lattice field theories in two dimensions that includes gauge theories. Given a two dimensional orientable surface of genus $g$, the partition function $Z$ is defined for a triangulation consisting of $n$ triangles of area $\epsilon$. The reason these models are called quasi-topological is that $Z$ depends on $g$, $n$ and $\epsilon$ but not on the details of the triangulation. They are also soluble in the sense that the computation of their partition functions can be reduced to a soluble one dimensional problem. We show that the continuum limit is well defined if the model approaches a topological field theory in the zero area limit, i.e., $\epsilon \to 0$ with finite $n$. We also show that the universality classes of such quasi-topological lattice field theories can be easily classified. Yang-Mills and generalized Yang-Mills theories appear as particular examples of such continuum limits.
da Cunha Bruno G. Carneiro
Teotonio-Sobrinho Paulo
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