Monopole–antimonopole correlation functions in 4D U(1) gauge theory

Abstract

We study the two-point correlator of a modified Confined-Coulomb transition order parameter in four dimensional compact U (1) lattice gauge theory with Wilson action. Its long distance behavior in the confined phase turns out to be governed by a single particle decay. The mass of this particle is computed and found to be in agreement with previous calculations of the 0 ++ gaugeball mass. Remarkably, our order parameter allows to extract a good signal to noise ratio for masses with low statistics. The results we present provide a numerical check of a theorem about the structure of the Hilbert space describing the confined phase of four dimensional compact U (1) lattice gauge theories.

Dual superconductivity and vacuum properties in Yang–Mills theories

“…Results are summarized in Table II and our estimate for the correlation length, based on the determination at the largest value of β, is ξ = 0.11 ± 0.02 fm. We have also repeated our measurement using an alternative way to study the temporal correlator [21], obtaining a good agreement. We would like to stress the consistency of our results with those reported in Ref.…”

“…[21]. One reason for the problems encountered can be traced back to the small value of ξ itself (ξ ∼ 0.1 fm), which makes the signal to fade away very rapidly after a few lattice spacings.…”

“…The numerical study of the temporal correlator of µ as a mean to determine the monopole mass has already been considered for the U(1) pure gauge theory in 4 dimensions [12,21]. In the confined phase, where dual superconductivity is at work, µ = 0.…”

“…[21], and consists in considering a new observableρ, which is the derivative of ln μ(t, n)µ(0, n) with respect to the adimensional temporal distancet in place of the inverse gauge coupling β. The expected behaviour forρ can be easily derived from Eq.…”

Direct numerical computation of disorder parameters

“…While that is enough to test hi as a parameter for confinement, a direct determination could be useful in contexts like the study of its correlation functions [10,22,23]. The problem of dealing with extremely rare configurations can be approached using the idea of generalized ensembles [24 -26].…”