Lorentz Symmetry Breaking in $\mathcal{N} =2$ Superspace

TL;DR

This paper explores the effects of Lorentz symmetry breaking in three-dimensional $ =2$ supersymmetric theories by introducing a constant vector field, leading to a deformed superspace and modified propagators for perturbative analysis.

Contribution

It develops the $ =2$ aether superspace by deforming the supersymmetry generators, providing explicit propagators and enabling perturbative calculations in Lorentz-violating supersymmetric theories.

Findings

Derived explicit superspace propagators in deformed supersymmetry

Analyzed the deformed superalgebra structure

Performed perturbative calculations using the new propagators

Abstract

In this paper, we will study the deformation of a three dimensional theory with $\mathcal{N} =2$ supersymmetry. This theory will be deformed by the presence of a constant vector field. This deformation will break the Lorentz symmetry. So, we will analyse this theory using $\mathcal{N} =2$ aether superspace. The $\mathcal{N} =2$ aether superspace will be obtained from a deformation of the usual $\mathcal{N} =2$ superspace. This will be done by deforming the generators of the three dimensional $\mathcal{N} =2$ supersymmetry. After analysing this deformed superalgebra, we will derive an explicit expression for the superspace propagators in this deformed superspace. Finally, we will use these propagators for performing perturbative calculations.