Instantons or Monopoles? Dyons

TL;DR

This paper investigates the fate of instantons in non-abelian gauge theories after abelian projection, revealing they form closed dyon loops with quantized electric charge, impacting the understanding of Yang-Mills vacuum dynamics.

Contribution

It demonstrates that instantons become closed dyon loops with quantized electric charge after abelian projection in gauge theories.

Findings

Instantons are composed of closed dyon loops.

Electric charge of dyons is quantized.

Implications for Yang-Mills vacuum dynamics are discussed.

Abstract

Non-abelian gauge theories can be cast into abelian gauge theories with monopoles. We ask what becomes of the instantons after abelian projection. Instantons are found to consist of closed dyon loops. It is shown that the electric charge of the dyons is quantized. The implication of this result for the dynamics of the Yang-Mills vacuum is briefly discussed.