High Q BPS Monopole Bags are Urchins

TL;DR

This paper numerically constructs high-charge BPS monopole configurations in SU(2) gauge theory, revealing they resemble sea urchins with multiple peaks, and explores their approximate spherical symmetry at large Q, supporting Bolognesi's conjecture.

Contribution

It provides the first numerical evidence that high-charge BPS monopoles can form approximately spherically symmetric 'urchin-like' configurations, confirming Bolognesi's conjecture.

Findings

Configurations with Q=81 have energy exceeding the BPS bound by 54%.

Monopoles form Q cones with peaks, resembling sea urchins.

Energy scales roughly linearly with Q.

Abstract

It has been known for 30 years that 't Hooft-Polyakov monopoles of charge Q greater than one cannot be spherically symmetric. 5 years ago, Bolognesi conjectured that, at some point in their moduli space, BPS monopoles can become approximately spherically symmetric in the high Q limit. In this note we determine the sense in which this conjecture is correct. We consider an SU(2) gauge theory with an adjoint scalar field, and numerically find configurations with Q units of magnetic charge and a mass which is roughly linear in Q, for example in the case Q=81 we present a configuration whose energy exceeds the BPS bound by about 54 percent. These approximate solutions are constructed by gluing together Q cones, each of which contains a single unit of magnetic charge. In each cone, the energy is largest in the core, and so a constant energy density surface contains Q peaks and thus resembles a sea urchin. We comment on some relations between a non-BPS cousin of these solutions and the dark matter halos of dwarf spherical galaxies.