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

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