Shapes of magnetic monopoles in effective $SU(2)$ models

TL;DR

This paper systematically explores a family of effective $SU(2)$ models with an adjoint scalar, deriving analytic monopole solutions that exhibit complex energy density profiles, including hollow cores and multi-shell structures.

Contribution

It identifies model redundancies, constructs the BPS limit, and provides a method to generate analytic monopole solutions with novel energy density configurations.

Findings

Monopoles with hollow cores and shell-like energy distributions.

Analytic solutions generalizing the 't Hooft-Polyakov monopole.

Structured monopole solutions with multiple sub-shells.

Abstract

We present a systematic exploration of a general family of effective $SU(2)$ models with an adjoint scalar. First, we discuss a redundancy in this class of models and use it to identify seemingly different, yet physically equivalent models. Next, we construct the Bogomol'nyi-Prasad-Sommerfield (BPS) limit and derive analytic monopole solutions. In contrast to the 't Hooft-Polyakov monopole, included here as a special case, these solutions tend to exhibit more complex energy density profiles. Typically, we obtain monopoles with a hollow cavity at their core where virtually no energy is concentrated; accordingly, most of the monopole's energy is stored in a spherical shell around its core. Moreover, the shell itself can be structured, with several "sub-shells". A recipe for the construction of these analytic solutions is presented.