Universal Aspects of Two-Dimensional Yang-Mills Theory at Large N

Details Universal Aspects of Two-Dimensional Yang-Mills Theory at Large N Universal Aspects of Two-Dimensional Yang-Mills Theory at Large N

1995-01-21

arxiv.org/abs/hep-th/9501099v1

Int.J.Mod.Phys. A11 (1996) 1733-1746

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, plain TeX

Scientific paper

We show that the large N partition functions and Wilson loop observables of two-dimensional Yang-Mills theories admit a universal functional form irrespective of the gauge group. We demonstrate that U(N) QCD_2 undergoes a large N, third-order phase transition on the projective plane at an area-coupling product of \pi^2/2. We use this as a lemma to provide a direct transcription of the partition functions and phase portraits of Yang-Mills theory from the U(N) on RP^2 at large N to the other classical Lie groups on S^2. We compute the expectation value of the Wilson loops in the fundamental representation for SO(N) and Sp(N) on the two sphere. Finally we compare the strong- and weak-coupling limit of these expressions with those found elswhere in the literature.

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