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_{coul} (p) ~ d^2(p) f(p)/p^2 are calculated. For large momenta p, the gluon propagator decreases like 1/p^{1+\eta} with \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 \sigma_{coul} \ge \sigma comes close to be saturated. Finally, we provide evidence that the ghost form factor d(p) and f(p) acquire IR singularities, i.e., d(p) \propto 1/\sqrt{p} and f(p) \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.