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Register a new userPropagators in lattice Coulomb gauge and confinement mechanisms
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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.
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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 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 is, like that of the transverse gluon, IR divergent, thus effectively extending the Gribov-Zwanziger scenario to full QCD.
We calculate the lattice quark propagator in Coulomb gauge both from dynamical and quenched configurations. We show that in the continuum limit both the static and full quark propagator are multiplicatively renormalizable. From the propagator we extract the quark renormalization function Z(|p|) and the running mass M(|p|) and extrapolate the latter to the chiral limit. We find that M(|p|) practically coincides with the corresponding Landau gauge function for small momenta. The computation of M(|p|) can be however made more efficient in Coulomb gauge; this can lead to a better determination of the chiral mass and the quark anomalous dimension. Moreover from the structure of the full propagator we can read off an expression for the dispersion relation of quarks, compatible with an IR divergent effective energy. If confirmed on larger volumes this finding would allow to extend the Gribov-Zwanziger confinement mechanism to the fermionic sector of QCD.
We present SU(3) gluon propagators calculated on 48*48*48*N_t lattices at beta=6.8 where N_t=64 (corresponding the confinement phase) and N_t=16 (deconfinement) with the bare gauge parameter,alpha, set to be 0.1. In order to avoid Gribov copies, we employ the stochastic gauge fixing algorithm. Gluon propagators show quite different behavior from those of massless gauge fields: (1) In the confinement phase, G(t) shows massless behavior at small and large t, while around 5<t<15 it behaves as massive particle, and (2) effective mass observed in G(z) becomes larger as z increases. (3) In the deconfinement phase, G(z) shows also massive behavior but effective mass is less than in the confinement case. In all cases, slope masses are increasing functions of t or z, which can not be understood as addtional physical poles.
We propose to investigate infrared properties of gluon and ghost propagators related to the so-called Gribov-Zwanziger confinement scenario, originally formulated for Landau and Coulomb gauges, for other gauges as well. We present results of our investigation of SU(2) lattice gauge theory in the maximally Abelian gauge (MAG), focusing on the behavior of propagators in the off-diagonal (i.e. non-Abelian) sector. We also comment on our preliminary results for general linear covariant gauges, in particular for Feynman gauge.
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