Instantons in 4-dimensional gauged O(5) Skyrme models

TL;DR

This paper studies instanton solutions in a four-dimensional gauged O(5) sigma model, revealing a relationship between topological charges and solutions like BPST instantons and winding number configurations.

Contribution

It introduces a new class of solutions characterized by two topological charges in a gauged O(5) sigma model, expanding understanding of instantons in higher-dimensional gauge theories.

Findings

BPST instantons with zero winding number and unit Chern-Pontryagin charge.

Solutions with unit winding number have zero Chern-Pontryagin charge.

Numerical integration of spherically symmetric equations reveals properties of these solutions.

Abstract

We consider a family of four-dimensional non-linear sigma models based on an O(5) symmetric group, whose fields take their values on the 4-sphere S4. An SO(4)-subgroup of the model is gauged. The solutions of the model are characterised by two distinct topological charges, the Chern-Pontryagin charge of the gauge field and the degree of the map, i.e. the winding number, of the S4 field. The one dimensional equations arising from the variation of the action density subjected to spherical symmetry are integrated numerically. Several properties of the solutions thus constructed are pointed out. The only solution with unit Chern-Pontryagin charge are the usual BPST instantons with zero S4 winding number, while solutions with unit S4 winding number have zero Chern-Pontryagin charge.