The Central Charge in 3D Simple Superalgebra

TL;DR

This paper investigates the emergence of a central charge in the N=1 supersymmetry algebra in 3D, highlighting the exclusive contribution of the matter sector and extending the analysis to gauge fields with Chern-Simons terms.

Contribution

It demonstrates that in 3D N=1 supersymmetry, only the matter sector contributes to the central charge, unlike the N=2 case, and extends the analysis to include gauge fields with Chern-Simons terms.

Findings

Central charge arises only from matter sector in N=1 supersymmetry.

Extension of the model to include gauge fields with Chern-Simons term.

Contrast with N=2 supersymmetry where gauge fields also contribute.

Abstract

A matter self-interacting model with N=1-supersymmetry in 3D is discussed in connection with the appearance of a central charge in the algebra of the supersymmetry generators. The result is extended to include gauge fields with a Chern-Simons term. The main result is that, for a simple supersymmetry, only the matter sector contributes to the central charge in contrast to what occurs in the N=2 case.