Polyakov-Loops and Fermionic Zero Modes in QCD2 on the Torus

Details Polyakov-Loops and Fermionic Zero Modes in QCD2 on the Torus Polyakov-Loops and Fermionic Zero Modes in QCD2 on the Torus

1996-11-14

arxiv.org/abs/hep-th/9611105v3

Nucl.Phys. B514 (1998) 381-398

Physics

High Energy Physics

High Energy Physics - Theory

some comments added and some typos corrected, 17 pages, Latex, 2 figures

Scientific paper

10.1016/S0550-3213(97)00733-5

A simple derivation of the free energy and expectation values of Polyakov-loops in $QCD_2$ via path integral methods is given. In the chosen gauge (which can be generalized to 4 dimensions) without Gribov-copies the Fadeev-Popov determinant and the integration over the space component of the gauge field cancel exactly and we are left only with an integration over the zero components of the gauge field in the Cartan sub-algebra. This way the Polyakov-loop operators become Vertex-operators in a simple quantum mechanical model. The number of fermionic zero modes is related to the winding-numbers of $A_0$ in this gauge.

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