Supersymmetric Monopole Quantum Mechanics on Sphere

TL;DR

This paper investigates N=2 supersymmetric quantum mechanics of a charged particle on a sphere with a Dirac monopole, using a CP(1) model approach to analyze the spectrum and supersymmetry breaking conditions.

Contribution

It introduces a gauge covariant chiral superfield formalism to study monopole interactions without singularities and derives conditions for supersymmetry breaking.

Findings

Supersymmetry can be spontaneously broken depending on monopole charge and operator ordering.

Explicit spectrum calculation for the supersymmetric monopole system.

Conditions for supersymmetry breaking are expressed in terms of quantized parameters.

Abstract

We study N=2 supersymmetric quantum mechanics of a charged particle on sphere in the background of Dirac magnetic monopole. We adopt CP(1) model approach in which the monopole interaction is free of singularity. In order to exploit manifest U(1) covariance in the superspace formalism, we introduce a gauge covariant chiral superfield which is annihilated by the gauge covariant superderivative instead of the usual superderivative. We carry out the quantization of the resulting system and compute the quantum mechanical spectrum. We obtain the condition for the spontaneous breaking of supersymmetries explicitely in terms of the monopole charge and a parameter characterizing the operator ordering ambiguity. We find that the supersymmetry is spontaneously broken unless a certain combination of theses quantities satisfies some quantization condition.