Propagators in Coulomb gauge from SU(2) lattice gauge theory

Abstract

A thorough study of 4-dimensional SU(2) Yang-Mills theory in Coulomb gauge is performed using large scale lattice simulations. The (equal-time) transverse gluon propagator, the ghost form factor $d(p)$ and the Coulomb potential ${V}_{\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{l}}(p)\ensuremath{\propto}{d}^{2}(p)f(p)/{p}^{2}$ are calculated. For large momenta $p$, the gluon propagator decreases like $1/{p}^{1+\ensuremath{\eta}}$ with $\ensuremath{\eta}=0.5(1)$. At low momentum, the propagator is weakly momentum dependent. The small momentum behavior of the Coulomb potential is consistent with linear confinement. We find that the inequality ${\ensuremath{\sigma}}_{\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{l}}\ensuremath{\ge}\ensuremath{\sigma}$ is satisfied. Finally, we provide evidence that the ghost form factors $d(p)$ and $f(p)$ acquire IR singularities, i.e., $d(p)\ensuremath{\propto}1/\sqrt{p}$ and $f(p)\ensuremath{\propto}1/p$, respectively. It turns out that the combination ${g}_{0}^{2}{d}_{0}(p)$ of the bare gauge coupling ${g}_{0}$ and the bare ghost form factor ${d}_{0}(p)$ is finite and therefore renormalization group invariant.