An all-order proof of the equivalence between Gribov's no-pole and Zwanziger's horizon conditions
Abstract
The quantization of non-Abelian gauge theories is known to be plagued by Gribov copies. Typical examples are the copies related to zero modes of the Faddeev-Popov operator, which give rise to singularities in the ghost propagator. In this work we present an exact and compact expression for the ghost propagator as a function of external gauge fields, in SU (N) Yang-Mills theory in the Landau gauge. It is shown, to all orders, that the condition for the ghost propagator not to have a pole, the so-called Gribov's no-pole condition, can be implemented by demanding a non-vanishing expectation value for a functional of the gauge fields that turns out to be Zwanziger's horizon function. The action allowing to implement this condition is the Gribov-Zwanziger action. This establishes in a precise way the equivalence between Gribov's no-pole condition and Zwanziger's horizon condition.
- Publication:
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Physics Letters B
- Pub Date:
- February 2013
- DOI:
- 10.1016/j.physletb.2013.01.039
- arXiv:
- arXiv:1212.2419
- Bibcode:
- 2013PhLB..719..448C
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 11 pages, typos corrected, version accepted for publication in Phys. Lett. B