The local structure of topological charge fluctuations in QCD

We introduce the Dirac eigenmode filtering of topological charge density associated with Ginsparg-Wilson fermions as a tool to investigate the local structure of topological charge fluctuations in QCD. The resulting framework is used to demonstrate that the bulk of topological charge in QCD does not appear in the form of unit quantized lumps. This means that the mixing of "would-be" zeromodes associated with such lumps is probably not the prevalent microscopic mechanism for spontaneous chiral symmetry breaking in QCD. To characterize the coherent local behavior in topological charge density at low energy, we compute the charges contained in maximal coherent spheres enclosing non-overlapping peaks. We find a continuous distribution essentially ending at approximate to 0.5. Finally, we study, for the first time, the overlap-operator topological-charge- density-correlators and find consistency with non-positivity at nonzero physical distance. This represents a non-trivial check on the locality (in gauge paths) of the overlap Dirac operator for realistic gauge backgrounds.