Twisted supersymmetric invariant formulation of Chern-Simons gauge theory on a lattice

We propose a twisted supersymmetric (SUSY) invariant formulation of the Chern-Simons theory on a Euclidean three-dimensional lattice. The SUSY algebra to be realized on the lattice is the N ¼ 4 D ¼ 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 the 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.