Ghost propagator and the Coulomb form factor from the lattice

TL;DR

This paper computes the Coulomb ghost propagator and potential in SU(2) Yang-Mills theory on the lattice, finding infrared enhancement and a string tension larger than the Wilson tension, supporting the Gribov-Zwanziger confinement scenario.

Contribution

It provides lattice calculations of the Coulomb ghost propagator and potential with improved temporal resolution, confirming key features predicted by the Gribov-Zwanziger confinement mechanism.

Findings

Ghost propagator is infrared enhanced with exponent ~0.5

Coulomb potential has a string tension about twice the Wilson tension

Results support the Coulomb scaling scenario from Gribov-Zwanziger theory

Abstract

We calculate the Coulomb ghost propagator G(|p|) and the static Coulomb potential V_C(|r|) for SU(2) Yang-Mills theory on the lattice. In view of possible scaling violations related to deviations from the Hamiltonian limit we use anisotropic lattices to improve the temporal resolution. We find that the ghost propagator is infrared enhanced with an exponent kappa_gh ~ 0.5 while the Coulomb potential exhibits a string tension larger than the Wilson string tension, sigma_C ~ 2 sigma. This agrees with the Coulomb "scaling" scenario derived from the Gribov-Zwanziger confinement mechanism.