Classical skyrmions in SU(N)/SO(N) cosets

TL;DR

This paper constructs and analyzes classical skyrmion solutions in SU(N)/SO(N) coset spaces, revealing their properties, masses, and symmetries for different N values, with implications for topological solitons.

Contribution

It provides explicit constructions and mass calculations of skyrmions in SU(N)/SO(N) cosets, highlighting differences for N=3 and N≥4, and clarifies their topological classifications.

Findings

For N=3, two distinct skyrmions with different winding numbers and shapes are identified.

For N≥4, only one spherical skyrmion exists, which is lighter than the N=3 solutions.

The mass and symmetry properties depend on the homotopy group structure of the coset.

Abstract

We construct the skyrmion solutions appearing in the coset spaces SU(N)/SO(N) for N > 2 and compute their classical mass. For N = 3, the third homotopy group pi_3(SU(3)/SO(3)) = Z_4 implies the existence of two distinct solutions: the skyrmion of winding number two has spherical symmetry and is found to be the lightest non-trivial field configuration; the skyrmion and antiskyrmion of winding number plus and minus one are slightly heavier and of toroidal shape. For N >= 4, there is only one skyrmion since the third homotopy group is Z_2. It is found to have spherical symmetry and is significantly lighter than the N = 3 solutions.