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arXiv · 1212.2419

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

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

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M. A. L. Capri, D. Dudal, M. S. Guimaraes, L. F. Palhares, S. P. Sorella. 2013-01-31. An all-order proof of the equivalence between Gribov's no-pole and Zwanziger's horizon conditions. https://doi.org/10.1016/j.physletb.2013.01.039

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