Magnetic monopole loops generated from two-instanton solutions: Jackiw-Nohl-Rebbi versus 't Hooft instanton

TL;DR

This paper compares magnetic monopole loops generated by JNR and 't Hooft two-instanton solutions in SU(2) Yang-Mills theory, showing their compatibility through deformation analysis in the instanton limit.

Contribution

It demonstrates how magnetic monopole loops from JNR instantons deform into those from 't Hooft instantons, resolving previous apparent contradictions.

Findings

JNR two-instanton generates a magnetic monopole loop.

't Hooft two-instanton does not generate a monopole loop.

Monopole loops from JNR instantons deform into those from 't Hooft instantons in the limit.

Abstract

In our previous paper (Fukui et al., 2010), we have shown that the Jackiw-Nohl-Rebbi two-instanton generates a circular loop of magnetic monopole in the four-dimensional Euclidean SU(2) Yang-Mills theory. On the other hand, it is claimed in Brower, Orginos and Tan (1997) that the 't Hooft two-instanton does not generate magnetic monopole loop. It seems that two results are inconsistent with each other, since the JNR two-instanton converges to the 't Hooft two-instanton in a certain limit. In this paper, we clarify that two results are compatible with each other by demonstrating how the magnetic monopole loop generated from the JNR two-instanton deforms in the process of taking the 't Hooft two-instanton limit.