Supersymmetric Chern-Simons Vortex Systems and Extended Supersymmetric Quantum Mechanics Algebras

TL;DR

This paper explores the supersymmetric quantum mechanics structures underlying N=2 supersymmetric Chern-Simons vortex systems, revealing extended supersymmetry algebras and their effects on zero modes and fluctuations.

Contribution

It uncovers an N=4 extended supersymmetric algebra in vortex zero modes and analyzes how supersymmetric terms influence the Dirac operator index and bosonic fluctuations.

Findings

Zero modes form an N=4 supersymmetric algebra with central charge.

Adding soft supersymmetric terms affects the Dirac operator index.

Underlying supersymmetry impacts bosonic fluctuation properties.

Abstract

We study N=2 supersymmetric Chern-Simons Higgs models in $(2+1)$-dimensions and the existence of extended underlying supersymmetric quantum mechanics algebras. Our findings indicate that the fermionic zero modes quantum system in conjunction with the system of zero modes corresponding to bosonic fluctuations, are related to an N=4 extended 1-dimensional supersymmetric algebra with central charge, a result closely connected to the N=2 spacetime supersymmetry of the total system. We also add soft supersymmetric terms to the fermionic sector in order to examine how this affects the index of the corresponding Dirac operator, with the latter characterizing the degeneracy of the solitonic solutions. In addition, we analyze the impact of the underlying supersymmetric quantum algebras to the zero mode bosonic fluctuations. This is relevant to the quantum theory of self-dual vortices and particularly for the symmetries of the metric of the space of vortices solutions and also for the non-zero mode states of bosonic fluctuations.