  We study the influence of center vortices on the low-lying eigenmodes of the
Dirac operator, in both the overlap and asqtad formulations. For
center-projected configurations, one finds that the low-lying near-zero modes
are present in the staggered (asqtad) formulation, but not in the overlap and
"chirally-improved" formulations. We argue that this is due to the absence of a
field-independent chiral symmetry in the latter formulations, when the Dirac
operator is evaluated on the very rough configurations generated by center
projection. We also confirm and extend the results of Kovalenko et al. [Phys.
Lett. B 648, 383 (2007)], finding strong correlations between center vortex
locations, and the scalar density of low-lying Dirac eigenmodes on unprojected
lattices, in both asqtad and overlap formulations. It is found that the
low-lying eigenmodes have their largest concentrations in point-like regions,
rather than on submanifolds of higher dimensionality.
