1212.2419 (M. A. L. Capri et al.)

An all-order proof of the equivalence between Gribov's no-pole and
Zwanziger's horizon conditions    [PDF]

M. A. L. Capri, D. Dudal, M. S. Guimaraes, L. F. Palhares, S. P. Sorella

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 nonvanishing 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.

View original: http://arxiv.org/abs/1212.2419