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

TL;DR

This paper investigates the Gribov ambiguity in 1+1 dimensional gauge theories on a cylinder, revealing a complex vacuum structure and its implications for phenomena like chiral condensates and anomalies.

Contribution

It provides an explicit analysis of the Gribov problem in gauge theories on a cylinder, showing the resulting non-trivial physical state structure and connections to chiral symmetry breaking.

Findings

Gauge orbit space is an orbifold.

Proper treatment of Gribov ambiguity affects physical states.

Chiral condensate arises from spectral flow and anomalies.

Abstract

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.