Chern-Simons Theory in SIM(1) Superspace

TL;DR

This paper develops a three-dimensional supersymmetric Chern-Simons theory within SIM(1) superspace, demonstrating how Lorentz symmetry breaking reduces supersymmetry from N=1 to N=1/2 and formulating the theory using simplified SIM(1) superfields.

Contribution

It introduces the first construction of an N=1/2 supersymmetric Chern-Simons theory on a boundaryless manifold using SIM(1) superspace formalism.

Findings

Formulated Chern-Simons action with SIM(1) superfields.

Analyzed gauge symmetry of the N=1/2 supersymmetric theory.

Demonstrated supersymmetry breaking from N=1 to N=1/2 due to Lorentz symmetry reduction.

Abstract

In this paper, we will analyse a three dimensional supersymmetric Chern-Simons theory in SIM(1) superspace formalism. The breaking of the Lorentz symmetry down to the SIM(1) symmetry, breaks half the supersymmetry of the Lorentz invariant theory. So, the supersymmetry of the Lorentz invariant Chern-Simons theory with N=1 supersymmetry will break down to N=1/2 supersymmetry, when the Lorentz symmetry is broken down to the SIM(1) symmetry. First, we will write the Chern-Simons action using SIM(1) projections of N=1 superfields. However, as the SIM(1) transformations of these projections are very complicated, we will define SIM(1) superfields which transform simply under SIM(1) transformations. We will then express the Chern-Simons action using these SIM(1) superfields. Furthermore, we will analyse the gauge symmetry of this Chern-Simons theory. This is the first time that a Chern-Simons theory with N=1/2 supersymmetry will be constructed on a manifold without a boundary.