Broken planar Skyrmions -- statics and dynamics

TL;DR

This paper explores the static structures and dynamic behaviors of broken planar Skyrmions, revealing their polyform configurations for various N and analyzing how their constituent partons interact during evolution.

Contribution

It extends the understanding of broken planar Skyrmions for larger N and introduces the first numerical simulations of their dynamics, linking parton interactions to overall behavior.

Findings

Polyform structures persist for larger N

Parton interactions govern dynamic behavior

Comparison with standard Skyrme model highlights differences

Abstract

The broken planar Skyrme model is a theory that breaks global O(3) symmetry to the dihedral group D_N. It has been shown that the single soliton solution is formed of N constituent parts, named partons, that are topologically confined. The multi-soliton solutions have already been computed for N = 3 and were shown to be related to polyiamonds. We extend this for larger N and demonstrate that this polyform structure continues (planar figures formed by regular N-gons joined along their edges, of which polyiamonds are the N=3 subset). Furthermore, we numerically simulate the dynamics of this model for the first time. It will be demonstrated that the time dependent behaviour of these solutions can be broken down into the interactions of its constituent partons. The results are then compared with those of the standard planar Skyrme model.