Chern-Simons theory on the lattice

TL;DR

This paper introduces novel lattice formulations of the Chern-Simons term, using fermion determinants and gauge terms, with modified parity symmetry that preserves the continuum limit.

Contribution

It proposes new lattice representations of the Chern-Simons term that maintain continuum properties while modifying lattice parity symmetry.

Findings

Lattice Chern-Simons term constructed from fermion determinants.

Direct lattice construction from Abelian gauge terms.

Parity symmetry is modified on the lattice without affecting the continuum limit.

Abstract

We present new proposals for the representation of a Chern-Simons term on the lattice. In the first part, such a term is constructed from the fermion determinant, and in the second part directly from the Abelian gauge term. In both cases, the parity transformation is modified on the lattice without affecting its continuum limit.