From hermitian matrix model to lattice gauge theory

Details From hermitian matrix model to lattice gauge theory From hermitian matrix model to lattice gauge theory

1992-09-24

arxiv.org/abs/hep-th/9209097v1

Physics

High Energy Physics

High Energy Physics - Theory

8pages, Latex

Scientific paper

I consider a lattice model of a gauge field interacting with matrix-valued scalars in $D$ dimensions. The model includes an adjustable parameter $\s$, which plays role of the string tension. In the limit $\s=\infty$ the model coincides with Kazakov-Migdal's ``induced QCD", where Wilson loops obey a zero area law. The limit $\s=0$, 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.

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