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29 March 2024
 
  » arxiv » hep-lat/9209003

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Chern-Simons Currents and Chiral Fermions on the Lattice
Maarten Golterman ; Karl Jansen ; David Kaplan ;
Date 1 Sep 1992
Journal Phys.Lett. B301 (1993) 219-223
Subject hep-lat hep-th
AbstractWe compute the Chern-Simons current induced by Wilson fermions on a $d=2n+1$ dimensional lattice, making use of a topological interpretation of the momentum space fermion propagator as a map from the torus to the sphere, $T^{d} o S^{d}$. These mappings are shown to fall in different homotopy classes depending on the value of $m/r$, where $m$ is the fermion mass and $r$ is the Wilson coupling. As a result, the induced Chern-Simons term changes discontinuously at $d+1$ different values for $m$, unlike in the continuum. This behavior is exactly what is required by the peculiar spectrum found for a recently proposed model of chiral lattice fermions as zeromodes bound to a domain wall.
Source arXiv, hep-lat/9209003
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