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

TL;DR

This paper classifies fractional instantons and bions in the SU(N) principal chiral model on R^2×S^1 with twisted boundary conditions, revealing their structures, charges, and relations to Yang-Mills theory, advancing understanding of non-perturbative effects.

Contribution

It provides a detailed classification of fractional instantons and bions, including their topological charges and configurations, in the principal chiral model with twisted boundary conditions, and establishes a connection to Yang-Mills theory.

Findings

Fractional instantons are global vortices with twisted U(1) moduli.

For Z_N symmetric boundary conditions, instanton numbers are 1/N; for generic conditions, they are irrational.

Neutral bions have zero instanton charge, while charged bions can have non-zero instanton charge.

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 ${\mathbb R}^2 \times S^1$ 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.