Polyakov loops and fermionic zero-modes in QCD2 on the torus Original Research Article

A direct derivation of the free energy and expectation values of Polyakov loops in QCD2 via path integral methods is given. The chosen gauge fixing has no Gribov copies and has a natural extension to four dimensions. The Faddeev-Popov determinant and the integration over the space component of the gauge field cancel exactly. It only remains 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 Ao in this gauge.