Dynamical Domain Wall Defects in 2+1 Dimensions

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.Comment: 12 pages, Late

A doubled discretisation of abelian Chern-Simons theory

A new discretisation of a doubled, i.e. BF, version of the pure abelian Chern-Simons theory is presented. It reproduces the continuum expressions for the topological quantities of interest in the theory, namely the partition function and correlation function of Wilson loops. Similarities with free spinor field theory are discussed which are of interest in connection with lattice fermion doubling.Comment: 5 pages, revtex, 2 ps figures (epsf required). To appear in Phys.Rev.Let

The 3d Ising Model represented as Random Surfaces

We consider a random surface representation of the three-dimensional Ising model.The model exhibit scaling behaviour and a new critical index \k which relates \g_{string} for the bosonic string to the exponent \a of the specific heat of the 3d Ising model is introduced. We try to determine \k by numerical simulations.Comment: No figures included. Available by ordinary mail on request. 13 pages. Latex. preprint NBI-HE-92-8

The XXZ Heisenberg model on random surfaces

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