Gribov ambiguity

In gauge theory, especially in non-abelian gauge theories, global problems at gauge fixing are often encountered. 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,[1] Heinzl's paper with a quantum-mechanical toy example,[2] and the second slide of Kondo's presentation.[3]

References

  1. ↑ V. N. Gribov. Quantization of non-abelian gauge theories. Nuclear Physics B139 (1978), p.1-19
  2. ↑ T. Heinzl. Hamiltonian Approach to the Gribov Problem. Nuclear Physics B (Proc.Suppl) 54A (1997) 194-197, arXiv:hep-th/9609055,
  3. ↑ http://www.icra.it/MG/mg12/talks/sqg5_kondo.pdf