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 t
he 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.
We review our lattice results concerning the Gribov-Zwanziger confinement mechanism in Coulomb gauge. In particular, we verify the validity of Gribovs IR divergence condition for the Coulomb ghost form factor. We also show how the quark self-energy i
s, like that of the transverse gluon, IR divergent, thus effectively extending the Gribov-Zwanziger scenario to full QCD.
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.
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.
We discuss the gluon propagator in 3- and 4-dimensional Yang-Mills theories in Coulomb gauge and compare it with the corresponding Landau gauge propagator, showing that for both the relevant IR mass scale coincides. We also report preliminary results
on Coulomb gauge ghost form factor and quark propagators and give a comment on the gluon propagators strong coupling limit.
We investigate an extension to the phase shift formalism for calculating one-loop determinants. This extension is motivated by requirements of the computation of Z-string quantum energies in D=3+1 dimensions. A subtlety that seems to imply that the v
acuum polarization diagram in this formalism is (erroneously) finite is thoroughly investigated.
