Fuzzy Supersphere and Supermonopole

TL;DR

This paper explores the quantum geometry of a charged particle on a supersphere with a supermonopole, revealing fuzzy supersphere structures and supersymmetric degeneracies in the lowest Landau level.

Contribution

It constructs a supermonopole via a supersymmetric Hopf map and analyzes the resulting algebraic structures and wavefunctions, extending noncommutative geometry to supersymmetric settings.

Findings

Coordinates form a fuzzy supersphere in the lowest Landau level

Existence of two types of degenerate wavefunctions due to supersymmetry

Ground state wavefunctions are described by Hopf spinors

Abstract

It is well-known that coordinates of a charged particle in a monopole background become noncommutative. In this paper, we study the motion of a charged particle moving on a supersphere in the presence of a supermonopole. We construct a supermonopole by using a supersymmetric extension of the first Hopf map. We investigate algebras of angular momentum operators and supersymmetry generators. It is shown that coordinates of the particle are described by fuzzy supersphere in the lowest Landau level. We find that there exist two kinds of degenerate wavefunctions due to the supersymmetry. Ground state wavefunctions are given by the Hopf spinor and we discuss their several properties.