A Ginsparg-Wilson Approach to Lattice Chern-Simons Theory

Details A Ginsparg-Wilson Approach to Lattice Chern-Simons Theory A Ginsparg-Wilson Approach to Lattice Chern-Simons Theory

2003-05-07

arxiv.org/abs/hep-lat/0305006v1

Physics

High Energy Physics

High Energy Physics - Lattice

17 pages, Latex, no figures

Scientific paper

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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