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

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

2004-07-24

arxiv.org/abs/hep-th/0407210v3

Phys.Rev. D71 (2005) 114019

Physics

High Energy Physics

High Energy Physics - Theory

12 pages,(v2) some new references and minor changes to the text, clarifying comments added, no changes in results. (v3)Title m

Scientific paper

10.1103/PhysRevD.71.114019

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.

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