Understanding the U(1) problem through dyon configuration in the Abelian projection

TL;DR

This paper demonstrates that dyons, arising from magnetic monopoles in the Abelian projection, can resolve the U(1) problem by dominating the topological susceptibility, aligning with the Veneziano–Witten formula.

Contribution

It introduces an Abelian-projected effective gauge theory incorporating dyons, derived from SU(2) Yang-Mills theory with a vacuum angle, to address the U(1) problem.

Findings

Dyons significantly contribute to topological susceptibility.

The effective theory aligns with the Veneziano–Witten formula.

The approach provides a new perspective on the U(1) problem.

Abstract

We show that the magnetic monopole promoted to the dyon due to the vacuum angle $\theta$ resolves the U(1) problem in the sense that the dyon obtained in this way gives a dominant contribution to the topological susceptibility. For this purpose, we derive an Abelian-projected effective gauge theory written in terms of Abelian degrees of freedom, which is obtained by integrating out all the off-diagonal degrees of freedom involved in the SU(2) Yang-Mills theory with the vacuum angle $\theta$. We evaluate the topological susceptibility by estimating the classical part of the effective dyon action obtained by performing the duality transformation. The obtained result is consistent with the Veneziano--Witten formula.