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Two dimensional QCD is a one dimensional Kazakov-Migdal model | | M. Caselle
; A. D’Adda
; L. Magnea
; S. Panzeri
; | | Date: |
5 Apr 1993 | | Journal: | Nucl.Phys. B416 (1994) 751-770 | | Subject: | hep-th | | Abstract: | 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. | | Source: | arXiv, hep-th/9304015 | | Services: | Forum | Review | PDF | Favorites | |
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