N=0 Supersymmetry and the Non-Relativistic Monopole

TL;DR

This paper explores the algebraic structure of non-relativistic monopole theories, revealing exotic fermionic charges that mimic supersymmetry properties without actual supersymmetry, and demonstrates how supersymmetric methods can elucidate non-supersymmetric models.

Contribution

It introduces theories with exotic fermionic charges that resemble supersymmetry but do not possess it, and shows how supersymmetric techniques can analyze such non-supersymmetric systems.

Findings

Existence of exotic fermionic charges in non-supersymmetric theories.

Supersymmetric methods can be applied to understand non-supersymmetric monopole theories.

New algebraic properties of non-relativistic monopoles.

Abstract

We study some of the algebraic properties of the non-relativistic monopole. We find that we can construct theories that possess an exotic conserved fermionic charge that squares to the Casimir of the rotation group, yet do not possess an ordinary supersymmetry. This is in contrast to previous known examples with such exotic fermionic charges. We proceed to show that the presence of the exotic fermionic charge in the non-supersymmetric theory can nonetheless be understood using supersymmetric techniques, providing yet another example of the usefulness of supersymmetry in understanding non-supersymmetric theories.