Gribov no-pole condition, Zwanziger horizon function, Kugo-Ojima confinement criterion, boundary conditions, BRST breaking and all that

TL;DR

This paper unifies the Gribov-Zwanziger and Kugo-Ojima approaches to confinement in Yang-Mills theories, showing their equivalence through boundary conditions and discussing the implications for BRST symmetry breaking.

Contribution

It demonstrates that imposing the Kugo-Ojima criterion as a boundary condition leads to a renormalizable partition function equivalent to the Gribov-Zwanziger formulation, unifying two key confinement approaches.

Findings

Kugo-Ojima boundary condition modifies the partition function.

The modified partition function matches the Gribov-Zwanziger form.

BRST symmetry is softly broken in this framework.

Abstract

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.