High Energy Physics - Theory
[Submitted on 21 Mar 2015 (v1), last revised 19 Aug 2015 (this version, v2)]
Title:Fractional instantons and bions in the principal chiral model on ${\mathbb R}^2\times S^1$ with twisted boundary conditions
View PDFAbstract: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 ${\mathbb R}^2 \times S^1$ with twisted boundary conditions. We find that fractional instantons are global vortices wrapping around $S^1$ with their $U(1)$ moduli twisted along $S^1$, that carry $1/N$ instanton (baryon) numbers for the ${\mathbb Z}_N$ 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 ${\mathbb Z}_3$ 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.
Submission history
From: Muneto Nitta [view email][v1] Sat, 21 Mar 2015 18:02:02 UTC (70 KB)
[v2] Wed, 19 Aug 2015 16:16:44 UTC (71 KB)
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