Gribov ambiguity and non-trivial vacuum structure of gauge theories on a   cylinder
  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. 
E. Langmann and G. W. Semenoff