Dynamical Domain Wall Defects in 2+1 Dimensions

Details Dynamical Domain Wall Defects in 2+1 Dimensions Dynamical Domain Wall Defects in 2+1 Dimensions

1999-02-09

arxiv.org/abs/hep-th/9902065v1

Phys.Lett. B451 (1999) 31-37

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LateX

Scientific paper

10.1016/S0370-2693(99)00238-5

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.

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