Jackiw-Nohl-Rebbi two-instanton as a source of magnetic monopole loop

TL;DR

This paper shows that a specific two-instanton solution in SU(2) Yang-Mills theory creates a magnetic monopole loop, providing insights into quark confinement mechanisms.

Contribution

It demonstrates that the Jackiw-Nohl-Rebbi two-instanton solution uniquely generates magnetic monopole loops, unlike the one-instanton solution, advancing understanding of confinement.

Findings

Two-instanton solutions produce magnetic monopole loops.

One-instanton solutions in regular gauge do not produce such loops.

Results support the role of instantons and merons in quark confinement.

Abstract

We demonstrate that a Jackiw-Nohl-Rebbi solution as the most general two-instanton generates a circular loop of magnetic monopole in four-dimensional Euclidean SU(2) Yang-Mills theory, in contrast to the one-instanton solution in the regular gauge for which no such magnetic monopole loops exist. These results together with our previous result indicate that two-instanton solution and two-meron solution with the same asymptotic behavior in the long distance are responsible for quark confinement based on the dual superconductivity picture.