CLASSICAL-SOLUTIONS FOR 2-DIMENSIONAL QCD ON THE SPHERE

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. T his 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 fin d 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 criti cal behaviour for these new solutions. Finally, we describe solutions for lattice SU(N) which are in a sense dual to the continuum U(N) solu tions.