Instantons, monopoles, vortices, and the Faddeev-Popov operator eigenspectrum

Abstract

The relation of confinement scenarios based on topological configurations and the Gribov-Zwanziger scenario is examined. To this end the eigenspectrum of the central operator in the Gribov-Zwanziger scenario, the Faddeev-Popov operator, is studied in topological field configurations. It is found that instantons, monopoles, and vortices contribute to the spectrum in a qualitatively similar way. Especially, all give rise to additional zero-modes and thus can contribute to the Gribov-Zwanziger confinement mechanism. Hence a close relation between these confinement scenarios likely exists.

A first look at Landau-gauge propagators in G2Yang-Mills theory

“…In addition, it is not yet known how the two aspects, confinement due to topological field configurations and the GZKO mechanism, fit together. Only recently first investigations have pointed to a deep relationship [31,32,33,34,35].…”

Green's functions and topological configurations

“…In this gauge it was possible to show that vortices appear inside and on the boundary of the socalled first Gribov region [7], monopoles [8] and instantons [7] on the boundary of the first Gribov region, and instantons also on the common boundary of the first Gribov region and the so-called fundamental modular region [7]. According to the Gribov-Zwanziger scenario [12], these boundaries are responsible for the infrared properties of Green's functions.…”

“…However, at least vortices, instantons [7], and monopoles [8] can be transferred to Landau gauge, although they are not in one-to-one correspondence to their counterparts in other gauges [9]. Hence, in the following only Landau (and to some extent Coulomb) gauge will be discussed, despite its complexities [4,10,11].…”

“…An indirect indication for this is that the spectrum and eigenstates of the Faddeev-Popov operator, which determines the ghost propagator, are affected by topological configurations [7,8,13]. In particular, they give rise to additional zero-modes, which in principle enhances the ghost propagator.…”

Confinement encoded in Landau gauge gluon and ghost propagators

“…One can say that the global (not only infrared) behavior of the ghost dressing function is the closest relative to the confinement of quarks. Since vortex removal also removes all non-perturbative attributes [35] (percolating monopole trajectories, string tension, chiral condensate and the topological charge [31], it is very likely that the original divergence of the ghost propagator like 1/(q 2 ) 1+κ is mainly a result of the topological structure leading to an enhanced density of low-lying eigenvalues of M as demonstrated for MC [36] and model configurations [37].…”