Ribbons Around Mexican Hats

TL;DR

This paper studies quasi-topological solitons in a two-dimensional model with a mexican-hat potential, providing explicit solutions, stability conditions, and insights into their properties and destabilization mechanisms.

Contribution

It offers explicit solutions and stability analysis for quasi-topological solitons, highlighting their existence in weak coupling and the effects of gauge interactions.

Findings

Explicit soliton solutions derived

Stability conditions established in weak-coupling limit

Gauge interactions destabilize the solitons unless extended

Abstract

We analyze quasi-topological solitons winding around a mexican-hat potential in two space-time dimensions. They are prototypes for a large number of physical excitations, including Skyrmions of the Higgs sector of the standard electroweak model, magnetic bubbles in thin ferromagnetic films, and strings in certain non-trivial backgrounds. We present explicit solutions, derive the conditions for classical stability, and show that contrary to the naive expectation these can be satisfied in the weak-coupling limit. In this limit we can calculate the soliton properties reliably, and estimate their lifetime semiclassically. We explain why gauge interactions destabilize these solitons, unless the scalar sector is extended.