N=4 Supersymmetric Quantum Mechanics with Magnetic Monopole

TL;DR

This paper develops an N=4 supersymmetric quantum mechanics model for a charged particle on a sphere with a magnetic monopole, analyzing its symmetry algebra, energy spectrum, and supersymmetry breaking conditions.

Contribution

It introduces a novel N=4 supersymmetric quantum mechanics framework incorporating magnetic monopoles and explicitly calculates the symmetry algebra and energy spectrum.

Findings

Symmetry algebra is SU(1|2) x SU(2)

Hamiltonian expressed via SU(2) Casimir

Supersymmetry spontaneously broken to N=2 at certain monopole charges

Abstract

We propose an N=4 supersymmetric quantum mechanics of a charged particle on a sphere in the background of Dirac magnetic monopole and study the system using the CP(1) model approach. We explicitly calculate the symmetry algebra taking the operator ordering ambiguity into consideration. We find that it is given by the superalgebra SU(1|2)x SU(2). We show that the Hamiltonian can be written in terms of the Casimir invariant of SU(2). Using this relation and the lower bound for angular momentm we obtain the energy spectrum. We then examine the ground energy sector to find that the N=4 supersymmetry is spontaneously broken to N=2 for certain values of the monopole charge.