  We aim to offer a kind of unifying view on two popular topics in the studies
of nonperturbative aspects of Yang-Mills theories in the Landau gauge: the
so-called Gribov-Zwanziger approach and the Kugo-Ojima confinement criterion.
Borrowing results from statistical thermodynamics, we show that imposing the
Kugo-Ojima confinement criterion as a boundary condition leads to a modified
yet renormalizable partition function. We verify that the resulting partition
function is equivalent with the one obtained by Gribov and Zwanziger, which
restricts the domain of integration in the path integral within the first
Gribov horizon. The construction of an action implementing a boundary condition
allows one to discuss the symmetries of the system in the presence of the
boundary. In particular, the conventional BRST symmetry is softly broken.
