2-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 partial derivative0A0 = 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 g2 to one in exponentials of 1/g2. 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 we give explicitly the grand canonical partition function of such ensemble in terms of infinite products.