Half-monopoles and half-vortices in the Yang-Mills theory

TL;DR

This paper shows that smooth Yang-Mills potentials can represent monopoles and vortices with half-integer winding numbers, which are more common than the traditional integer-winding configurations like the 't Hooft-Polyakov monopole.

Contribution

It introduces the existence of smooth Yang-Mills configurations with half-integer winding numbers, expanding the understanding of monopole and vortex solutions.

Findings

Half-integer winding number monopoles and vortices exist in Yang-Mills theory.

Such configurations are generic compared to integer-winding solutions.

These solutions are smooth and physically relevant.

Abstract

It is demonstrated that there are smooth Yang-Mills potentials which correspond to monopoles and vortices of one-half winding number. They are the generic configurations, in contrast to the integral winding number configurations like the 't Hooft-Polyakov monopole.