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

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.

5 pages. v2 matches version to appear in PhysRevD (RC)

References in corpus (12)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach
• On the IR behaviour of the Landau-gauge ghost propagator
• Constraints on the IR behavior of the ghost propagator in Yang-Mills theories
• The Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge
• Gribov Copies in the Minimal Landau Gauge: the Influence on Gluon and Ghost Propagators
• More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
• Infrared behavior and Gribov ambiguity in SU(2) lattice gauge theory
• Electric-magnetic asymmetry of the A^2 condensate and the phases of Yang-Mills theory

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