Dynamical Domain Wall Defects in 2+1 Dimensions

TL;DR

This paper investigates the behavior of Dirac fermions with dynamic, curved domain wall defects in 2+1 dimensions, revealing how anomalies induce currents related to the defect's geometry, with implications for condensed matter systems.

Contribution

It extends the Callan-Harvey mechanism to arbitrary-shaped, moving defects and derives a geometric expression for anomaly-induced currents in such systems.

Findings

Chiral zero modes are localized on the defect's worldsheet.

Anomaly-induced currents depend on the defect's geometry and curvature.

The framework applies to condensed matter systems with fermionic defects.

Abstract

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.