On the interrelation between monopoles, vortices, topological charge and chiral symmetry breaking: an analysis using overlap fermions for SU(2)

TL;DR

This paper investigates how removing P-vortices and Abelian monopoles from lattice configurations affects topological charge and chiral symmetry breaking, using overlap fermions in SU(2), revealing their crucial roles.

Contribution

It demonstrates that removing vortices or monopoles eliminates topological charge and zero modes, highlighting their essential role in topological and chiral properties of the gauge configurations.

Findings

Zero modes disappear after vortex or monopole removal.

Topological susceptibility approaches zero without vortices or monopoles.

Modified ensembles show different smearing behavior compared to unmodified ones.

Abstract

We study the properties of configurations from which P-vortices on one hand or Abelian monopoles on the other hand have been removed. We find that the zero modes and the band of non-zero modes close to zero disappear from the spectrum of the overlap Dirac operator, confirming the absence of topological charge and quark condensate. The different behavior of the modified ensembles under smearing compared to the unmodified Monte Carlo ensemble corroborates these findings. The gluonic topological susceptibility rapidly approaches zero in accordance with Q_{index}=0. The remaining (ultraviolet) monopoles without vortices and -- to a less extent -- the remaining vortices without monopoles are unstable under smearing whereas smearing of the unmodified Monte Carlo ensemble effects the monopoles and vortices only by smoothing, reducing the density only slightly.