Reduction of Dynamical Degrees of Freedom in the Large-NGauge Theory

It is pointed out that the factorization of disconnected Wilson loop amplitudes implies a major reduction in the dynamical degrees of freedom in the large-N limit of lattice gauge theory; the original model may be replaced by a much simpler one (d is the space-time dimensionality), $Z={Π}{}{{μ}}[{∫} d {U}_{{μ}}exp({{β}}_{{ν}{≠}}{Σ}{d}{{μ}{≠}{ν}=1}tr{U}_{{μ}}{U}ᵥ{{U}_{{μ}}}^{{}}{{U}_{{ν}}}^{{}})]$ Thus the field theory may be reduced to an integration over a finite number of matrices in large-$N$ limit.