Two dimensional QCD is a one dimensional Kazakov-Migdal model

Details Two dimensional QCD is a one dimensional Kazakov-Migdal model Two dimensional QCD is a one dimensional Kazakov-Migdal model

1993-04-05

arxiv.org/abs/hep-th/9304015v2

Nucl.Phys. B416 (1994) 751-770

Physics

High Energy Physics

High Energy Physics - Theory

DFTT 15/93, 17 pages, Latex (Besides minor changes and comments added we note that for U(N) odd and even N have to be treated

Scientific paper

10.1016/0550-3213(94)90553-3

We calculate the partition functions of QCD in two dimensions on a cylinder and on a torus in the gauge $\partial_{0} A_{0} = 0$ 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 as an infinite product.

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