Large $N$ Phase Transition in Continuum QCD$_2$

Details Large $N$ Phase Transition in Continuum QCD$_2$ Large $N$ Phase Transition in Continuum QCD$_2$

1993-05-12

arxiv.org/abs/hep-th/9305047v1

Phys.Lett. B319 (1993) 219-230

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, preprint LPTENS-93/20 and RU-93-17

Scientific paper

10.1016/0370-2693(93)90806-S

We compute the exact partition function for pure continuous Yang-Mills theory on the two-sphere in the large $N$ limit, and find that it exhibits a large $N$ third order phase transition with respect to the area $A$ of the sphere. The weak coupling (small A) partition function is trivial, while in the strong coupling phase (large A) it is expressed in terms of elliptic integrals. We expand the strong coupling result in a double power series in $e^{-g^2 A}$ and $g^2 A$ and show that the terms are the weighted sums of branched coverings proposed by Gross and Taylor. The Wilson loop in the weak coupling phase does not show the simple area law. We discuss some consequences for higher dimensions.

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