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:
“Legends of prediction are common throughout the whole Household of Man. Gods speak, spirits speak, computers speak. Oracular ambiguity or statistical probability provides loopholes, and discrepancies are expunged by Faith.”
—Ursula K. Le Guin (b. 1929)