Gribov ambiguity and non-trivial vacuum structure of gauge theories on a cylinder

Details Gribov ambiguity and non-trivial vacuum structure of gauge theories on a cylinder Gribov ambiguity and non-trivial vacuum structure of gauge theories on a cylinder

1992-12-05

arxiv.org/abs/hep-th/9212038v3

Phys.Lett. B303 (1993) 303-307

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, a few typos and signs corrected, reference added

Scientific paper

10.1016/0370-2693(93)91436-Q

Using the hamiltonian framework, we analyze the Gribov problem for U(N) and SU(N) gauge theories on a cylinder (= (1+1) dimensional spacetime with compact space S^1). The space of gauge orbits is found to be an orbifold. We show by explicit construction that a proper treatment of the Gribov ambiguity leads to a highly non-trivial structure of all physical states in these quantum field theory models. The especially interesting example of massless QCD is discussed in more detail: There, some of the special static gauge transformations which are responsible for the Gribov ambiguity also lead to a spectral flow, and this implies a chiral condensate in all physical states. We also show that the latter is closely related to the Schwinger term and the chiral anomaly.

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