April 1993 TWO DIMENSIONAL QCD IS A ONE DIMENSIONAL KAZAKOV - MIGDAL MODEL

We calculate the partition functions of QCD in two dimensions on a cylinder and on a torus in the gauge ∂ 0 A 0 = 0 by integrating explicitly over the non zero modes of the Fourier expansion in the periodic time variable. The result is a one dimensional Kazakov-Migdal matrix model with eigenvalues on a circle rather than on a line. We prove that our result coincides with the standard expansion in representations of the gauge group. This involves a non trivial modular transformation from an expansion in exponentials of g 2 to one in exponentials of 1/g 2. Finally we argue that the states of the U (N) or SU (N) partition function can be interpreted as a gas of N free fermions, and the grand canonical partition function of such ensemble is given explicitly.