Lattice Coulomb propagators, effective energy and confinement

TL;DR

This paper demonstrates that lattice Coulomb gauge propagators support the Gribov-Zwanziger confinement mechanism, showing infrared enhancement and a diverging ghost form factor, with implications for understanding quark and gluon confinement.

Contribution

It provides a lattice Hamiltonian analysis confirming the IR behavior predicted by the Gribov-Zwanziger scenario and extracts the Coulomb string tension from the Coulomb potential.

Findings

IR enhanced effective energy for quarks and gluons

Diverging ghost form factor consistent with dual-superconducting vacuum

Coulomb string tension approximately twice the physical string tension

Abstract

We show that in the lattice Hamiltonian limit all Coulomb gauge propagators are consistent with the Gribov-Zwanziger confinement mechanism, with an IR enhanced effective energy for quarks and gluons and a diverging ghost form factor compatible with a dual-superconducting vacuum. Multiplicative renormalizability is ensured for all static correlators, while for non-static ones their energy dependence plays a crucial role in this respect. Moreover, from the Coulomb potential we can extract the Coulomb string tension \sigma_C ~ 2 \sigma.