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

Seikou Kato·Kei-Ichi Kondo
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Abstract

We show that the magnetic monopole promoted to the dyon due to the vacuum angle $θ$ 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 $θ$. 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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Seikou Kato, Kei-Ichi Kondo. 2005-04-20. Understanding the U(1) problem through dyon configuration in the Abelian projection. https://doi.org/10.1103/physrevd.71.114019

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