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

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.