Quasi-Topological Field Theories in Two Dimensions as Soluble Models

Abstract

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.

23 pages, 16 figures, uses psbox.tex

References in corpus (5)

• Two Dimensional Gauge Theories Revisited
• Lattice Topological Field Theory in Two Dimensions
• Structure of Topological Lattice Field Theories in Three Dimensions
• State Sum Models and Simplicial Cohomology
• The Cosmological Constant and Volume-Preserving Diffeomorphism Invariants

Cited by in corpus (4)

• 2D Quantum Double Models From a 3D Perspective
• Topological low-temperature limit of Z(2) spin-gauge theory in three dimensions
• On two-dimensional quasitopological field theories
• GL(2,R) dualities in generalised Z(2) gauge theories and Ising models