Quark propagation in the instantons of lattice QCD

Abstract

We quantitatively examine the extent to which instanton degress of freedom, contained within standard Monte-carlo generated gauge-field configurations, can maintain the characteristic features of the mass and renormalisation functions of the non-perturbative quark propagator. We use overimproved stout-link smearing to isolate instanton effects on the lattice. Using a variety of measures, we illustrate how gauge fields consisting almost solely of instanton-like objects are produced after only 50 sweeps of smearing. We find a full vacuum, with a packing fraction more than three times larger than phenomenological models predict. We calculate the overlap quark propagator on these smeared configurations, and find that even at high levels of smearing the majority of the characteristic features of the propagator are reproduced. We thus conclude that instantons contained within standard Monte-carlo generated gauge-field configurations are the degrees of freedom responsible for the dynamical generation of mass observed in lattice QCD.

Centre vortex removal restores chiral symmetry

“…On the vortex-removed ensemble, the majority of dynamical mass generation is gone, with only a small remnant reflected by both the pion and the rho having masses larger than twice the bare quark mass. This is consistent with our results for the vortex-removed quark propagator [26,27]. We note that while the rho is greatly reduced in mass, it is not degenerate with the pion, providing the first indication that we are within the chiral regime where physics beyond simple quark counting can contribute.…”

“…The vortex-only ensemble is able to reproduce all qualitative features of the spectrum, although masses are slightly lower. This is most likely an artifact of cooling [26,27,38]. Notably, in both cases the pion is much lighter than the rho, a clear signal that it retains its nature as a pseudo-Goldstone boson, and thus that dynamical chiral symmetry breaking is present on the vortex-only ensemble.…”

Double-winding Wilson loops and monopole confinement mechanisms

“…A difference-of-areas result can be obtained if one adds in off-diagonal gluons ("W-bosons") to the abelian models, but this also implies that the spatial distribution of abelian fields in models with W-bosons must be qualitatively different from the corresponding distributions in a monopole plasma, dyon gas, or dual superconductor. We have suggested that when W-bosons are added to such models, the result is a theory of center vortices (for some recent developments, see [30,31].) At least one must consider, in the context of models in which the confining fields are dominantly abelian, what sort of distribution of confining abelian field strength would be compatible with the difference-of-areas requirement for double-winding Wilson loops.…”

Instanton contributions to the low-lying hadron mass spectrum

“…The instanton content of the vacuum under the same overimproved stout-link smearing algorithm selected herein was also studied in Ref. [38]. To examine the extent to which the non-trivial topology identified on the lattice is consistent with instantons, two measures of the local maxima of the action density found on representative configurations were measured and compared to the classical instanton solution.…”