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

One can define generalized models of gaugino condensation as theories that dynamically break a discrete R symmetry but do not break supersymmetry. We consider general examples consisting of gauge and matter fields and the minimal number of gauge-singlet fields to avoid flat directions in the potential. We explore which R symmetries can arise and their spontaneous breaking. In general, we find that the discrete symmetry is ℤ 2b0R , and the number of supersymmetric vacua is b o , where b o is the coefficient of the one-loop beta function. Results are presented for various groups, including SU(N c ), SO(N c ), Sp(2N c ), and G 2 , for various numbers of flavors, N f , by several methods. This analysis can also apply to the other exceptional groups and, thus, all simple Lie groups. We also comment on model-building applications where a discrete R symmetry, broken by the singlet vacuum expectation values, can account for μ-type terms and allow a realistic Higgs spectrum naturally.