Electroweak multi-monopoles

TL;DR

This paper constructs and analyzes multi-charge electroweak monopole solutions, revealing their internal structure, phase bubbles, and magnetic properties, with implications for stability and energy finiteness when gravity is considered.

Contribution

It introduces the first multi-charge generalizations of electroweak monopoles and explores their detailed internal structure and phase configurations.

Findings

Monopoles have zero dipole but finite quadrupole moments.

Large-charge monopoles form symmetric phase bubbles with complex field configurations.

Electroweak monopoles have infinite energy, but gravity may render them finite.

Abstract

We construct the multi-charge generalizations for the electroweak magnetic monopole solution of Cho and Maison within a wide range of values of the magnetic charge. We use the same ansatz for the axially symmetric fields as the one previously employed to construct the electroweak sphalerons and compare the internal structure of monopoles with that of sphalerons. The monopoles have zero dipole moment but a finite quadrupole momentum that rapidly increases with growing magnetic charge. For large charges, the monopole configurations are strongly squashed and show inside a bubble of symmetric phase filled with a U(1) hypercharge field produced by a pointlike magnetic charge at the origin, strong enough to suppress all other fields and restore the full gauge symmetry. The bubble is surrounded by a large belt of broken phase containing a magnetically charged ring filled with a nonlinear W-condensate, squeezed between two superconducting rings of opposite electric currents. In the far field region there remains only the magnetic field supported by the total magnetic charge contained at the origin and in the magnetic ring. The axially symmetric monopoles are probably just a special case of more general monopole solutions not possessing any continuous symmetries. The Cho-Maison monopole is stable but the stability of its multi-charge generalizations is not yet confirmed. All electroweak monopoles have infinite energy due to the pointlike U(1) charge at the origin, but the energy is expected to become finite after taking gravity into account, which should provide a cutoff via creating an event horizon to shield the U(1) charge.