Gribov horizon and BRST symmetry: a few remarks

The issue of the BRST symmetry in presence of the Gribov horizon is addressed in Euclidean Yang-Mills theories in the Landau gauge. The positivity of the Faddeev-Popov operator within the Gribov region enables us to convert the soft breaking of the BRST invariance exhibited by the Gribov-Zwanziger action into a non-local exact symmetry, displaying explicit dependence from the non-perturbative Gribov parameter. Despite its non-locality, this symmetry turns out to be useful in order to establish non-perturbative Ward identities, allowing us to evaluate the vacuum expectation value of quantities which are BRST exact. These results are generalized to the refined Gribov-Zwanziger action introduced in [1], which yields a gluon propagator which is non-vanishing at the origin in momentum space, and a ghost propagator which is not enhanced in the infrared.