Gribov Ambiguity: Non-Abelian Theories & Solutions

[Bobhawke]

Im looking for a good resource that clearly explains the problem of Gribov ambiguity. In particular, I want to know
1. Why the problem only arises for non-abelian theories
2. Why restricting the functional integration to field configurations where the Faddeev-popov determinant is positive solves the problem for perturbative theories
3. Why this doesn't work for non-perturbative theories

Thanks in advance

 

[Haelfix]

I had hep-th/0504095 in my bookmarks on this subject as well as the original paper. Alternatively most textbooks on qft usually has a section on the problem. there's also been quite a bit about the subject from mathematical physicists depending on what your preferences are.

Its really one of those persistent problems (like the Landau ghost) that really hasn't gone away and you always have to keep it in mind (especially when dealing with complicated vacuum structures with nontrivial topology and where you are interested in nonpertubative physics)

 

[Lester]

Lattice computations of gluon and ghost propagators seem to show that Gribov ambiguity is not a concern in the infrared limit. Indeed, ghost propagator is that of a free particle. This matter is hotly debated yet as it would imply that a lot of work about gauge theories is wrong and does not describe the correct behavior of the theory as was believed for several years.

As Gribov copies are not relevant even in the ultraviolet limit, this question seems no relevant at all for non-Abelian gauge theories. Some effects are seen on lattice at finite volume in the intermediate energy region.

Jon

 

[Haelfix]

Thats actually been known for a long time I gather. That certain subclasses of lattice models miss the Gribov ambiguity as well as some topological defects/ambiguities in certain field theories.

That doesn't bother me too much, I actually wouldn't expect generic lattice simulations to pick them up without some ahh tweaking, but some people vehemently disagree with this.

 

[Haelfix]

After eyeballing the literature based on another comment, I should amend the statement -- I'm way out of the loop in this field. Once upon a time there was a problem (the effect on the nonperturbative physics based on lattice simulations yielded small, rather than large corrections contrary to expectations), but the modern literature actually seems to have 180'd and now there doesn't seem to be much of a conflict anymore between phenomenology expectations and lattice results (at least with respect to gluon propagators). Indeed they see many Gribov copies.