Calculating Gluino Condensates in $\mathcal{N}=1$ SYM from Seiberg-Witten Curves

Abstract

We determine the gluino condensate $< \Tr \lambda^2 >$ in the pure ${\cal N}=1$ super Yang-Mills theory (SYM) for the classical gauge groups $SU(r+1)$, $SO(2r+1)$, $USp(2r)$ and $SO(2r)$, by deforming the pure ${\cal N}=2$ SYM theory with the adjoint scalar multiplet mass, following the work by Finnell and Pouliot, and Ritz and Vainshtein. The value of the gluino condensate agrees in all cases with what was found in the weak coupling istanton calculation.