Dyon Loops and Abelian Instantons

TL;DR

This paper constructs Abelian gauge field configurations called Abelian instantons, generated by magnetic worldlines, and embeds them in a UV-complete theory, revealing their relation to traditional instantons and dyon loops.

Contribution

It introduces a novel class of Abelian instantons generated by magnetic worldlines and demonstrates their embedding in a UV-complete model, linking them to known instanton solutions.

Findings

Abelian instantons are generated by closed magnetic worldlines with non-trivial winding.

Full instanton charge resides in the unbroken U(1) sector within the Georgi-Glashow model.

Euclidean dyon loops can be continuously deformed into small BPST instantons.

Abstract

We construct Abelian gauge field configurations that carry non-zero instanton number. Each such "Abelian instanton" is generated by a closed magnetic worldline in four-dimensional Euclidean space, provided the Abelian gauge field has non-trivial winding along the closed worldline. The resulting field configuration corresponds to a Euclidean dyon loop featuring non-zero instanton number. We embed these dyon loops in a UV-complete theory using the Georgi-Glashow model and show that the full instanton charge is borne entirely by the unbroken $U(1)$ sector. In this same model, using a numerical relaxation procedure, we show that Euclidean dyon loops are a continuous deformation of small BPST instantons.