TY - JOUR

T1 - Dynamical domain wall defects in 2 + 1 dimensions

AU - Fosco, C. D.

AU - Fradkin, E.

AU - López, A.

N1 - Funding Information:
This work begun during a visit of EF to Instituto de Fı́sica Balseiro and he thanks A. Garcı́a from for his kind hospitality. We acknowledge F.A. Schaposnik for useful comments and references. C.D.F. and A.L. thank the members of the Department of Physics of the University of Oxford where part of this work was done. This work was supported in part by CONICET, The British Council, Fundación Antorchas, and ANPCyT (Argentina) (CF and AL) and by the National Science Foundation grant No. DMR98-17941 at the University of Illinois at Urbana-Champaign (EF).

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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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U2 - 10.1016/S0370-2693(99)00238-5

DO - 10.1016/S0370-2693(99)00238-5

M3 - Article

AN - SCOPUS:0002933997

VL - 451

SP - 31

EP - 37

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 1-2

ER -