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arXiv · hep-th/9301065

A Simple Model Inducing QCD

I. Ya. Aref'eva
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Abstract

A simple lattice model inducing a gauge theory is considered. The model describes an interaction of a gauge field to an $N\times N$ complex matrix scalar field transforming as a field in the fundamental representation. In contrast to the Kazakov-Migdal model the model contains only the linear interaction between scalar and gauge lattice fields. This model does not suffer from extra local U(1) symmetries. In an approximation of a translation invariant master field the large N limit of the model is investigated. At large N the gauge fields can be integrated out yielding an effective theory describing an interaction of eigenvalues of the master field. The reduced model exhibits phase transitions at the points $β_{\bar {cr}}$ and $β_{\underline{cr}}$ and the region $(β_{\bar{cr}}, β_{\underline{cr}})$ separates the strong and weak regions of the model. To study the behaviour of the model at large $N$ in more systematic way the quenched momentum prescription with constraints for treating the large N limit of gauge theories is used. With the help of the technique of orthogonal polynomials nonlinear equations describing the large N limit of the reduced model {\it with quenching} are presented.

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I. Ya. Aref'eva. 1993-01-16. A Simple Model Inducing QCD. https://doi.org/10.1016/0370-2693(93)91296-y

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