Non-Bogomolny SU(N) BPS Monopoles

TL;DR

This paper constructs new static monopole solutions for SU(N) Yang-Mills-Higgs theories that are not derived from the Bogomolny equations, interpreted as monopole-anti-monopole configurations using harmonic maps.

Contribution

It introduces a novel class of non-Bogomolny monopole solutions for SU(N) with N>2, expanding the understanding of monopole configurations beyond the first-order equations.

Findings

Solutions are spherically symmetric monopole-anti-monopole configurations.

Construction involves harmonic maps into complex projective spaces.

Solutions exist for N>2, not satisfying Bogomolny equations.

Abstract

For N>2 we present static monopole solutions of the second order SU(N) BPS Yang-Mills-Higgs equations which are not solutions of the first order Bogomolny equations. These spherically symmetric solutions may be interpreted as monopole anti-monopole configurations and their construction involves harmonic maps into complex projective spaces.