Dyon Loops and Abelian 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.