Sphalerons and Strings

TL;DR

This paper explores the electromagnetic properties of sphalerons, revealing their dipole moments originate from circulating currents and magnetic charges, and compares different definitions of electromagnetic fields within the Standard Model.

Contribution

It provides a detailed analysis of sphaleron electromagnetic structure and compares various field definitions, enhancing understanding of their topological and physical characteristics.

Findings

Sphaleron dipole moment arises from circulating electric currents and magnetic charges.

Magnetic charge in sphalerons has a topological origin linked to axisymmetry.

Comparison of electromagnetic field definitions in the Standard Model.

Abstract

This work is based on a paper with Margaret James, to appear in Phys Rev D. In it we showed that the dipole moment of the sphaleron has its origin in two components: a ring of electric current circulating around the edge of the sphaleron; and also two regions of opposite magnetic charge above and below the ring. This magnetic charge has a partly topological explanation, arising from the fact that the sphaleron is axisymmetric and parity invariant. Here, I discuss the definition of the electromagnetic field and its sources in the Standard Model, comparing the one we use with the better-known one of 't Hooft. I also discuss the resemblance between the sphaleron and Nambu's ``dumb-bell'' -- a segment of $Z$-string which connects a monopole to an antimonopole.