Interrelation between monopoles, vortices, topological charge, and chiral symmetry breaking: Analysis using overlap fermions for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>

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 nonzero 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 ${Q}_{\mathrm{index}}=0$. 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 affects the monopoles and vortices only by smoothing, reducing the density only slightly.