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A Ginsparg-Wilson Approach to Lattice Chern-Simons Theory

W. Bietenholz·P. Sodano
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Abstract

The concept of lattice modified symmetry formulations is adapted to the parity symmetry of gauge fields and applied to the pure Abelian Chern-Simons action in three dimensions. We derive an analogue of the Ginsparg-Wilson relation for the parity anti-symmetry, which is motivated from the perfect lattice action, and which we denote as the Chern-Simons-Ginsparg-Wilson relation (CSGWR). In addition to the overlap type solutions, we construct explicitly simple and local polynomial solutions to the CSGWR. We show that these actions are exactly invariant under a lattice modified parity transformation. That transformation is local as well, and it turns into the standard parity transformation in the continuum limit.

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BibTeXRIS

W. Bietenholz, P. Sodano. 2003-05-07. A Ginsparg-Wilson Approach to Lattice Chern-Simons Theory. https://arxiv.org/abs/hep-lat/0305006

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