Off-Shell Extended Supersymmetries and Lorentz-Violating Abelian Gauge Models

TL;DR

This paper develops off-shell N=2 and N=4 supersymmetric extensions of an Abelian gauge model with Lorentz-violating Chern-Simons term, using dimensional reduction from higher dimensions and superspace formalism.

Contribution

It introduces a novel off-shell supersymmetric formulation of Lorentz-violating gauge models via dimensional reduction and superspace techniques.

Findings

Off-shell N=2 and N=4 supersymmetric models constructed.

Dimensional reduction from 6D and 10D yields consistent SUSY extensions.

Auxiliary fields ensure off-shell closure of the superalgebra.

Abstract

In this work, we propose the N=2 and N=4 supersymmetric extensions realized off-shell of the Abelian gauge model with Chern-Simons Lorentz-breaking term. We start with the theory in 6 and 10 dimensions and reduce \`{a} la Scherk the space-like coordinates to carry out the D=5 model in both cases. Then, we reduce the fifth space-like coordinate using the Legendre transformation technique for dimensional reduction. The last reduction method provides us with auxiliary fields that yield the superalgebra closed off-shell. Since the reduced bosonic Lagrangians from $6D$ and $10D$ are the same as the N=2 and N=4 SUSY-versions of the theory, respectively, we use the superspace-superfield formalism in N=1 to achieve the supersymmetric version of model.