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Fractional instantons and bions in the principal chiral model on \( {\mathrm{\mathbb{R}}}^2\times {S}^1 \) with twisted boundary conditions

  • Muneto Nitta
Open Access
Regular Article - Theoretical Physics

Abstract

Bions are multiple fractional instanton configurations with zero instanton charge playing important roles in quantum field theories on a compactified space with a twisted boundary condition. We classify fractional instantons and bions in the SU(N) principal chiral model on \( {\mathrm{\mathbb{R}}}^2\times {S}^1 \) with twisted boundary conditions. We find that fractional instantons are global vortices wrapping around S1 with their U(1) moduli twisted along S1, that carry 1/N instanton (baryon) numbers for the \( {\mathrm{\mathbb{Z}}}_N \) symmetric twisted boundary condition and irrational instanton numbers for generic boundary condition. We work out neutral and charged bions for the SU(3) case with the \( {\mathrm{\mathbb{Z}}}_3 \) symmetric twisted boundary condition. We also find for generic boundary conditions that only the simplest neutral bions have zero instanton charges but instanton charges are not canceled out for charged bions. A correspondence between fractional instantons and bions in the SU(N) principal chiral model and those in Yang-Mills theory is given through a non-Abelian Josephson junction.

Keywords

Solitons Monopoles and Instantons Sigma Models Field Theories in Lower Dimensions 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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© The Author(s) 2015

Authors and Affiliations

  1. 1.Department of Physics, and Research and Education Center for Natural SciencesKeio UniversityYokohamaJapan

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