On rotational excitations and axial deformations of BPS monopoles and Julia-Zee dyons

TL;DR

This paper demonstrates that Julia-Zee dyons cannot have slowly rotating excitations or axial dipole deformations, by analyzing stationary excitations and zero modes in a gauge-invariant harmonic decomposition.

Contribution

It provides a comprehensive analysis showing the non-existence of rotational and axial deformations in Julia-Zee dyons through gauge-invariant zero mode parametrization.

Findings

Julia-Zee dyons do not admit slowly rotating excitations.

No axial dipole deformations are present.

Zero modes are parametrized in a gauge-invariant manner.

Abstract

It is shown that Julia-Zee dyons do not admit slowly rotating excitations. This is achieved by investigating the complete set of stationary excitations which can give rise to non-vanishing angular momentum. The relevant zero modes are parametrized in a gauge invariant way and analyzed by means of a harmonic decomposition. Since general arguments show that the solutions to the linearized Bogomol'nyi equations cannot contribute to the angular momentum, the relevant modes are governed by a set of electric and a set of non self-dual magnetic perturbation equations. The absence of axial dipole deformations is also established.