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

TL;DR

This study uses large-scale lattice simulations to analyze SU(2) Yang-Mills theory in Coulomb gauge, revealing the behavior of gluon propagators, ghost form factors, and the Coulomb potential, supporting confinement and renormalization invariance.

Contribution

It provides detailed lattice results for propagators and potentials in Coulomb gauge, highlighting IR singularities and the near-saturation of the Coulomb string tension inequality.

Findings

Gluon propagator decreases as 1/p^{1+η} with η≈0.5 at high momenta

Coulomb potential behavior consistent with linear confinement at low momenta

Ghost form factor and f(p) exhibit IR singularities, proportional to 1/√p and 1/p respectively

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.