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arXiv · hep-lat/9209003

Chern-Simons Currents and Chiral Fermions on the Lattice

Maarten Golterman·Karl Jansen·David Kaplan
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Abstract

We 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, $T^{d}\to S^{d}$. 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.

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Maarten Golterman, Karl Jansen, David Kaplan. 1992-09-01. Chern-Simons Currents and Chiral Fermions on the Lattice. https://doi.org/10.1016/0370-2693(93)90692-b

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