In gauge theory, especially in non-abelian gauge theories, we often encounter global problems when gauge fixing. Gauge fixing means choosing a representative from each gauge orbit. The space of representatives is a submanifold and represents the gauge fixing condition. Ideally, every gauge orbit will intersect this submanifold once and only once. Unfortunately, this is often impossible globally for non-abelian gauge theories because of topological obstructions and the best that can be done is make this condition true locally. A gauge fixing submanifold may not intersect a gauge orbit at all or it may intersect it more than once. This is called a Gribov ambiguity (named after Vladimir Gribov).
Gribov ambiguities lead to a nonperturbative failure of the BRST symmetry, among other things.
A way to resolve the problem of Gribov ambiguity is to restrict the relevant functional integrals to a single Gribov region whose boundary is called a Gribov horizon.
See also the original paper of Gribov, Heinzl's paper with a quantum-mechanical toy example, and the second slide of Kondo's presentation.
Famous quotes containing the word ambiguity:
“Indeed, it is that ambiguity and ambivalence which often is so puzzling in women—the quality of shifting from child to woman, the seeming helplessness one moment and the utter self-reliance the next that baffle us, that seem most difficult to understand. These are the qualities that make her a mystery, the qualities that provoked Freud to complain, “What does a woman want?””
—Lillian Breslow Rubin (20th century)