Extended Supersymmetries and 2+1 Dimensional Supersymmetric Chern Simons Theories

TL;DR

This paper explores the underlying supersymmetric algebraic structures in N=2 supersymmetric Chern-Simons Higgs models in (2+1) dimensions, revealing an extended N=4 supersymmetry with central charge.

Contribution

It uncovers the N=4 extended supersymmetric algebra structure underlying fermionic zero modes and bosonic fluctuations in these models.

Findings

Fermionic zero modes form an N=2 supersymmetric quantum mechanics algebra.

Bosonic fluctuation zero modes also form an N=2 algebra.

These algebras combine to produce an N=4 extended supersymmetry with a central charge.

Abstract

We study N=2 supersymmetric Chern-Simons Higgs models in $(2+1)$-dimensions. As we will demonstrate, an extended supersymmetric quantum mechanics algebras underlies the fermionic zero modes quantum system and the zero modes corresponding to bosonic fluctuations. These two algebras, in turn, combine to give an N=4 extended 1-dimensional supersymmetric algebra with central charge