Winding number versus Chern--Pontryagin charge

TL;DR

This paper introduces a new class of Higgs models where soliton stability is governed by the winding number of the Higgs field rather than Chern-Pontryagin charges, allowing for more flexible gauge group choices.

Contribution

It proposes Higgs models stabilized by winding number, independent of gauge group, expanding the framework for topological solitons in gauge theories.

Findings

Stability of solitons linked to winding number rather than Chern-Pontryagin charge.

Models applicable to SO(N) gauge groups with 2 ≤ N ≤ d.

Potential for new topological soliton solutions in Higgs models.

Abstract

In the usual d dimensional SO(d) gauged Higgs models with $d$-component Higgs fields, the 'energies' of the topologically stable solitons are bounded from below by the Chern-Pontryagin charges. A new class of Higgs models is proposed here, whose 'energies' are stabilised instead by the winding number of the Higgs field itself, with no reference to the gauge group. Consequently, such Higgs models can be gauged by SO(N), with 2 \le N \le d.