Ribbons around Mexican Hats

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.