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

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 Vcoul(p)∝d²(p)f(p)/p² are calculated. For large momenta p, the gluon propagator decreases like 1/p^1+η with η=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 σcoul≥σ is satisfied. Finally, we provide evidence that the ghost form factors $d(p)$ and $f(p)$ acquire IR singularities, i.e., d(p)∝1/√p and f(p)∝1/p, respectively. It turns out that the combination g₀²d₀(p) of the bare gauge coupling g₀ and the bare ghost form factor d₀(p) is finite and therefore renormalization group invariant.