An all-order proof of the equivalence between Gribov%26apos;s no-pole and Zwanziger%26apos;s horizon conditions

作者：Capri M A L; Dudal D; Guimaraes M S^*; Palhares L F; Sorella S P

来源：Physics Letters B, 2013, 719(4-5): 448-453.

DOI：10.1016/j.physletb.2013.01.039

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%26apos;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%26apos;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%26apos;s no-pole condition and Zwanziger%26apos;s horizon condition.