From hermitian matrix model to lattice gauge theory

Abstract

I consider a lattice model of a gauge field interacting with matrix-valued scalars in $D$ dimensions. The model includes an adjustable parameter $\text{s}$, which plays role of the string tension. In the limit $\text{s}=\infty$ the model coincides with Kazakov-Migdal's ``induced QCD", where Wilson loops obey a zero area law. The limit $\text{s}=0$, where Wilson loops $W(C)=1$ independently of the size of the loop, corresponds to the Hermitian matrix model. For $D=2$ and $D=3$ I show that the model obeys the same combinatorics as the standard LGT and therefore one may expect the area law behavior. In the strong coupling expansion such a behavior is demonstrated.

Comments: 8pages, Latex