Horizon function in Landau gauge QCD revisited -- Free boundary case from viewpoint of network QCD --

TL;DR

This paper revisits the horizon function in Landau gauge QCD under free boundary conditions, clarifying its derivation, the horizon condition's pointwise validity, and its relation to the Kugo-Ojima criterion within the Gribov-Zwanziger framework.

Contribution

It provides a detailed review of the second type horizon function, demonstrating its pointwise validity under free boundary conditions and connecting it to the Kugo-Ojima criterion.

Findings

Horizon condition holds pointwise for each gauge configuration.

The horizon condition and Kugo-Ojima criterion coincide in the continuum limit.

Identity relations on networks explain the horizon condition's validity.

Abstract

In Gribov-Zwanziger scenario of color confinement, Zwanziger proposed two types of horizon function in lattice Landau gauge, the first one and the second one of which foundation was discussed in detail. The second type horizon function is focussed on in the present study. Its derivation and the horizon condition are briefly reviewed along the line of Zwanziger, and it is also reviewed that this horizon condition and Kugo-Ojima color confinement criterion coincide in the continuum limit. In case of free boundary condition in contrast to periodic boundary condition, it was shown that the horizon condition holds for each gauge fixed configuration in Landau gauge. It is clarified that this fact can be derived from some identity relation which holds on an arbitrary network of links in Landau gauge. Thus the origin of the pointwise validity of horizon condition is highlighted.