Existence of spinning solitons in gauge field theory

TL;DR

This paper investigates whether classical spinning solitons exist in Yang-Mills-Higgs theory, showing that for symmetric gauge fields, angular momentum can be expressed as surface integrals, and proving that known topological solitons do not admit stationary spinning excitations.

Contribution

The paper introduces a method to express angular momentum as surface integrals for symmetric gauge fields and proves the nonexistence of spinning excitations in known topological solitons within this framework.

Findings

Angular momentum can be expressed as surface integrals for symmetric gauge fields.

No stationary, axially symmetric spinning solitons exist for known topological solutions in SU(2) gauge theory.

Abstract

We study the existence of classical soliton solutions with intrinsic angular momentum in Yang-Mills-Higgs theory with a compact gauge group $\mathcal{G}$ in (3+1)-dimensional Minkowski space. We show that for \textit{symmetric} gauge fields the Noether charges corresponding to \textit{rigid} spatial symmetries, as the angular momentum, can be expressed in terms of \textit{surface} integrals. Using this result, we demonstrate in the case of $\mathcal{G}=SU(2)$ the nonexistence of stationary and axially symmetric spinning excitations for all known topological solitons in the one-soliton sector, that is, for 't Hooft--Polyakov monopoles, Julia-Zee dyons, sphalerons, and also vortices.