Dynamical domain wall defects in 2+1 dimensions

We study some dynamical properties of a Dirac field in 2 + 1 dimensions wit h spacetime dependent domain wall defects. We show that the Callan and Harv ey 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 o n 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 ano malies for fermions on surfaces embedded in higher dimensional spacetimes, we show that the chiral anomaly for this two dimensional theory is responsi ble 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, whi ch can be expressed entirely in terms of the spacetime curvature of the def ects. We discuss the application of this framework to fermionic systems wit h defects in condensed matter. (C) 1999 Published by Elsevier Science B.V. All rights reserved.