Classical Solutions for Two Dimensional QCD on the Sphere

Details Classical Solutions for Two Dimensional QCD on the Sphere Classical Solutions for Two Dimensional QCD on the Sphere

1993-09-22

arxiv.org/abs/hep-th/9309119v1

Nucl.Phys.B422:172-194,1994

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, CERN-TH-7016, UVA-HET-93-08

Scientific paper

10.1016/0550-3213(94)00153-7

We consider $U(N)$ and $SU(N)$ gauge theory on the sphere. We express the problem in terms of a matrix element of $N$ free fermions on a circle. This allows us to find an alternative way to show Witten's result that the partition function is a sum over classical saddle points. We then show how the phase transition of Douglas and Kazakov occurs from this point of view. By generalizing the work of Douglas and Kazakov, we find other `stringy' solutions for the $U(N)$ case in the large $N$ limit. Each solution is described by a net $U(1)$ charge. We derive a relation for the maximum charge for a given area and we also describe the critical behavior for these new solutions. Finally, we describe solutions for lattice $SU(N)$ which are in a sense dual to the continuum $U(N)$ solutions. (Parts of this paper were presented at the Strings '93 Workshop, Berkeley, May 1993.)

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