3 Skyrmions

We now move on to one dimension higher, and study Skyrmions. In recent years,

there has been a lot of interest in what people call “Skyrmions”, but what they

are studying is a 2-dimensional variant of the original idea of Skyrmions. These

occur in certain exotic magnetic systems. But instead, we are going to study the

original Skyrmions as discovered by Skyrme, which have applications to nuclear

physics.

With details to be filled in soon, hadronic physics exhibits (approximate)

spontaneously broken chiral symmetry

SO

unbroken group is (diagonal)

This symmetry is captured in various effective field theories of pions (which

are the approximate Goldstone bosons) and heavier mesons. It is also a feature

of QCD with very light u and d quarks.

The special feature of Skyrmion theory is that we describe nucleons as solitons

in the effective field theory. Skyrme’s original idea was that nucleons and bigger

nuclei can be modelled by classical approximations to some “condensates” of

pion fields. To explain the conservation of baryon number, the classical field

equations have soliton solutions (Skyrmions) with an integer topological charge.