Signals of confinement in Green functions of SU(2) Yang-Mills theory

TL;DR

This paper investigates how vortex removal in SU(2) Yang-Mills theory affects Green functions, revealing that vortices are crucial for confinement signals, as evidenced by changes in the running coupling, gluon, and ghost form factors.

Contribution

It demonstrates that vortex removal suppresses confinement signals in Green functions, linking vortex presence to the ghost singularity and Zwanziger's horizon condition.

Findings

Suppression of the running coupling and gluon form factor at low momenta after vortex removal.

Disappearance of ghost form factor singularity at zero momentum.

Vortex removal breaks Zwanziger's horizon condition for confinement.

Abstract

The vortex picture of confinement is employed to explore the signals of confinement in Yang-Mills Green functions. By using SU(2) lattice gauge theory, it has been well established that the removal of the center vortices from the lattice configurations results in the loss of confinement. The running coupling constant, the gluon and the ghost form factors are studied in Landau gauge for both cases, the full and the vortex removed theory. In the latter case, a strong suppression of the running coupling constant and the gluon form factor at low momenta is observed. At the same time, the singularity of the ghost form factor at vanishing momentum disappears. This observation establishes an intimate correlation between the ghost singularity and confinement. The result also shows that a removal of the vortices generates a theory for which Zwanziger's horizon condition for confinement is no longer satisfied.