Coulomb vs. physical string tension on the lattice

TL;DR

This paper investigates the relationship between Coulomb and Wilson string tensions on the lattice, revealing their decoupling at finite temperature and linking Coulomb confinement to the spatial string tension, especially across the deconfinement transition.

Contribution

It provides lattice evidence that Coulomb and Wilson string tensions decouple at finite temperature and explores their connection to the spatial string tension and deconfinement transition.

Findings

Coulomb and Wilson string tensions are related at zero temperature.

They decouple at finite temperature, with Coulomb confinement tied to the spatial string tension.

Alternative Coulomb potential definitions can sense the deconfinement transition.

Abstract

From continuum studies it is known that the Coulomb string tension $\sigma_C$ gives an upper bound for the physical (Wilson) string tension $\sigma_W$ [D. Zwanziger, Phys. Rev. Lett. 90, 102001 (2003)]. How does however such relationship translate to the lattice? In this paper we give evidence that there, while the two string tensions are related at zero temperature, they decouple at finite temperature. More precisely, we show that on the lattice the Coulomb gauge confinement scenario is always tied to the spatial string tension, which is known to survive the deconfinement phase transition and to cause screening effects in the quark-gluon plasma. Our analysis is based on the identification and elimination of center vortices which allows to control the physical string tension and study its effect on the Coulomb gauge observables. We also show how alternative definitions of the Coulomb potential may sense the deconfinement transition; however a true static Coulomb gauge order parameter for the phase transition is still elusive on the lattice.