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
ϵ
. The reason these models are called quasi-topological is that
Z
depends on
g
,
n
and
ϵ
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.,
ϵ→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.