  We study correlations between center vortices and the low-lying eigenmodes of
the Dirac operator, in both the overlap and asqtad formulations. In particular
we address a puzzle raised some years ago by Gattnar et al. [Nucl. Phys. B 716,
105 (2005)], who noted that the low-lying Dirac eigenmodes required for chiral
symmetry breaking do not appear to be present in center-projected
configurations. We show that the low-lying modes are in fact present in the
staggered (asqtad) formulation, but not in the overlap and ``chirally
improved'' formulations, and suggest a reason for this difference. We also
confirm and extend the results of Kovalenko et al. [Phys. Lett. B 648, 383
(2007)], showing that there is a correlation between center vortex locations,
and the scalar density of low-lying Dirac eigenmodes derived from unprojected
configurations. This correlation is strongest at points which are associated,
in the vortex picture, with non-vanishing topological charge density, such as
vortex intersection and ``writhing'' points. We present supporting evidence
that the lowest Dirac eigenmodes, in both asqtad and overlap formulations, have
their largest concentrations in point-like regions, rather than on submanifolds
of higher dimensionality.
