Chiral Symmetry Breaking in Supersymmetric Yang-Mills Theory

Abstract

It is proved that the contribution of self-dual twisted gauge configurations (torons) to the gluino condensate $〈\lambda \lambda 〉$ in $N=1\mathrm{}$ supersymmetric Yang-Mills theory remains finite in the thermodynamic limit. Using the richer vacuum structure of the theory, defined in a twisted box, the authors explain the constant value of the instanton contribution to the condensate $〈\lambda \lambda \mathrm{}\left(x\right)\mathrm{}\lambda \lambda \mathrm{}\left(y\right)\mathrm{}〉$. The physical picture obtained is consistent with $\mathrm{tr}{\mathrm{}(-1\mathrm{})\mathrm{}}^F$ and the effective-Lagrangian approach.