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One can define generalized models of gaugino condensation as theories whichdynamically break a discrete R-symmetry, but do not break supersymmetry. Weconsider general examples consisting of gauge and matter fields, and theminimal number of gauge singlet fields to avoid flat directions in thepotential. We explore which R-symmetries can arise, and their spontaneousbreaking. In general, we find that the discrete symmetry is$\mathbb{Z}_{2b_0R}$ and the number of supersymmetric vacua is $b_0$, where$b_0$ is the coefficient of the one-loop beta function. Results are presentedfor various groups, including $SU(N_c), SO(N_c), Sp(2N_c)$, and $G_2$, forvarious numbers of flavors, $N_f$, by several methods. This analysis can alsoapply to the other exceptional groups, and thus all simple Lie groups. We alsocomment on model building applications where a discrete R-symmetry, broken bythe singlet vevs, can account for $\mu$-type terms and allow a realistic Higgsspectrum naturally.

Generalized Gaugino Condensation in Super Yang-Mills Theories: Discrete R-Symmetries and Vacua