Dynamical supersymmetry breaking in supersymmetric QCD

The massless limit of supersymmetric QCD with $\text{N}{}_{\mathrm{?}}$ flavors and N colors is analyzed in detail. For $\text{N}{}_{\mathrm{?}}\text{< N}$ there is a unique superpotential which might be generated by non-perturbative effects. We show that it indeed appears, thus violating the non-renormalization theorems. For $\text{N}{}_{\mathrm{?}}\text{= N ? 1}$ instantons produce the superpotential. For $\text{N}{}_{\mathrm{?}}\text{< N ? 1}$ it is again generated, provided that a mild assumption about the dynamics of pure supersymmetric gauge theories is correct. For $\text{N}{}_{\mathrm{?}}\text{? N}$ no invariant superpotential exists; the classical vacuum degeneracy is a property of the full quantum theory. When a small quark mass term is added to the theory $\text{(}\text{for}\text{N}{}_{\mathrm{?}}\text{< N), N}$ supersymmetric ground states, identified with those found by Witten exist. As m → 0 these N vacua wander to infinity, leaving the massless theory without a ground state.