Vortex induced confinement and the IR properties of Green functions

In order to observe the confinement of quarks and gluons in Yang-Mills theory, two conditions must necessarily be obeyed [1]: (i) there must be a long range order of certain un–physical degrees of freedom (violation of the cluster decomposition ); (ii) there must be a mass gap for physical excitations. Using Landau gauge where the gauge configurations are restricted to the first Gribov regime, it was firstly speculated by Gribov [2] that the divergence of the ghost propagator at zero momentum transfer signals confinement. Over the years, Zwanziger has put forward that the configurations which are relevant for confinement are close to the Gribov horizon[3]. A formal relation between confinement and the IR properties of confinement was advocated by Kugo and Ojima [4]: their approach is based on the assumption that a unique definition of the BRST charge operator exists. This assumption, however, is invalidated by the presence of Gribov copies.