Geometry & Topology Seminar

Josh Cork, Leibniz University Hannover

"Gauged skyrmions"

The Skyrme model is a geometric model of nuclear physics in which nuclei are modelled by stable maps from space (R^3) into SU(2) which minimise an energy functional. These minima are called skyrmions. Unfortunately, despite some existence results, no analytic solutions are known. A surprisingly good approximation was provided by Atiyah and Manton, where the approximate skyrmion is the holonomy of a Yang-Mills instanton along all lines in one direction of R^4. Its accuracy was later explained by Sutcliffe, who showed that the Skyrme functional arises naturally from the Yang-Mills functional as the leading term in a mode expansion. An alternative to this approach is to instead consider a connection on S^1\times R^3, and take the holonomy around S^1, from which one obtains a natural way to couple skyrmions to a connection - a gauged skyrmion. In this talk we shall discuss this more general construction, and in particular how calorons - instantons on S^1\times R^3 - provide good approximations to minima, and how they may be used to calibrate the model towards a more physically realistic model for studying the electromagnetic properties of nuclei.

Zoom meeting: https://zoom.us/j/93859138328