BPS magnetic monopole bags

Abstract

We explore the characteristics of spherical bags made of large numbers of BPS magnetic monopoles. There are two extreme limits. In the Abelian bag, $N$ zeros of the Higgs field are arranged in a quasiregular lattice on a sphere of radius ${R}_{\mathrm{cr}}\ensuremath{\sim}N/v$, where $v$ is the Higgs vacuum expectation value. The massive gauge fields of the theory are largely confined to a thin shell at this radius that separates an interior with almost vanishing magnetic and Higgs fields from an exterior region with long-range Coulomb magnetic and Higgs fields. In the other limiting case, which we term a non-Abelian bag, the $N$ zeros of the Higgs field are all the origin, but there is again a thin shell of radius ${R}_{\mathrm{cr}}$. In this case the region enclosed by this shell can be viewed as a large monopole core, with small Higgs field but nontrivial massive and massless gauge fields.