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

22 pages, 5 figures; v2,v3 added references, v4 added two paragraphs and one figure in the summary

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Cited by in corpus (7)

• Restoration of supersymmetry on the lattice: Two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory
• Lattice Formulation of Two-Dimensional N=(2,2) SQCD with Exact Supersymmetry
• Two-dimensional N=(2,2) Supersymmetric Lattice Gauge Theory with Matter Fields in the Fundamental Representation
• Matrix formulation of superspace on 1D lattice with two supercharges
• Topologically Twisted $N=(2,2)$ Supersymmetric Yang-Mills Theory on Arbitrary Discretized Riemann Surface
• Deformed matrix models, supersymmetric lattice twists and N=1/4 supersymmetry
• Abelian Chern-Simons Gauge Theory on The Lattice