Fermion Zero Modes for Abelian BPS Monopoles

TL;DR

This paper analyzes fermion zero modes in abelian BPS monopoles, providing explicit solutions for arbitrary monopole charge and revealing their geometric structure when the charge exceeds one.

Contribution

It offers a detailed determination of normalisable zero modes for any monopole charge, highlighting their zero-line configurations for N>1.

Findings

Zero modes are explicitly determined for any monopole charge N.

For N>1, zero modes are zero along N-1 half-lines from the monopole.

The structure of zero modes depends on the monopole charge, revealing geometric patterns.

Abstract

Fermion zero modes for abelian BPS monopoles are considered. In the spherically symmetric case the normalisable zero modes are determined for arbitrary monopole charge N. If N>1 the zero modes are zero along $N-1$ half-lines emanating from the monopole.