Twisted SUSY Invariant Formulation of Chern-Simons Gauge Theory on a Lattice

TL;DR

This paper develops a lattice formulation of Chern-Simons theory that preserves twisted supersymmetry, enabling non-perturbative studies of topological gauge theories with complex gauge groups.

Contribution

It introduces a twisted SUSY invariant lattice formulation of Chern-Simons theory using N=4 D=3 algebra and oppositely oriented supercharges, maintaining manifest anti-hermiticity.

Findings

The lattice action corresponds to Landau gauge fixed Chern-Simons with complex gauge group.

The action decomposes into parity even and odd parts with distinct coefficients.

The formulation preserves twisted supersymmetry on the lattice.

Abstract

We propose a twisted SUSY invariant formulation of Chern-Simons theory on a Euclidean three dimensional lattice. The SUSY algebra to be realized on the lattice is the N=4 D=3 twisted algebra that was recently proposed by D'Adda et al.. In order to keep the manifest anti-hermiticity of the action, we introduce oppositely oriented supercharges. Accordingly, the naive continuum limit of the action formally corresponds to the Landau gauge fixed version of Chern-Simons theory with complex gauge group which was originally proposed by Witten. We also show that the resulting action consists of parity even and odd parts with different coefficients.