Domain wall fermions recover exact chiral symmetry in the infinite fifth dimension limit and produce an effective four-dimensional operator satisfying the Ginsparg-Wilson relation.
Chern-Simons Currents and Chiral Fermions on the Lattice
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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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Lecture notes on lattice methods for formal TASI students covering basics, confinement, chiral fermions, and case studies in the 3D Ising model and QCD.
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Domain wall fermions
Domain wall fermions recover exact chiral symmetry in the infinite fifth dimension limit and produce an effective four-dimensional operator satisfying the Ginsparg-Wilson relation.
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Lattice methods for students at a formal TASI
Lecture notes on lattice methods for formal TASI students covering basics, confinement, chiral fermions, and case studies in the 3D Ising model and QCD.