  We study some dynamical properties of a Dirac field in 2+1 dimensions with
spacetime dependent domain wall defects. We show that the Callan and Harvey
mechanism applies even to the case of defects of arbitrary shape, and in a
general state of motion. The resulting chiral zero modes are localized on the
worldsheet of the defect, an embedded curved two dimensional manifold. The
dynamics of these zero modes is governed by the corresponding induced metric
and spin connection. Using known results about determinants and anomalies for
fermions on surfaces embedded in higher dimensional spacetimes, we show that
the chiral anomaly for this two dimensional theory is responsible for the
generation of a current along the defect. We derive the general expression for
such a current in terms of the geometry of the defect, and show that it may be
interpreted as due to an "inertial" electric field, which can be expressed
entirely in terms of the spacetime curvature of the defects. We discuss the
application of this framework to fermionic systems with defects in condensed
matter.
