Supersymmetry Breaking and Metastability

Since Supersymmetry and String Theory: Beyond the Standard Model went to press, there have been a number of important developments in the subject of Dynamical Supersymmetry Breaking. These are reviewed here. 1 Dynamical Supersymmetry Breaking Models with Dynamical Supersymmetry Breaking (DSB) known for some time. But until recently, dynamical supersymmetry breaking seemed an exceptional phenomenon, involving chiral gauge theories with a special structure. The resulting particle physics models suffered from various deficiencies: • If DSB in a hidden sector in supergravity, gauginos light, and no amelioration of the flavor problems of ordinary supergravity theories. • If DSB at lower scale, gauge mediation. But resulting models quite complicated. Most models have DSB scale at least 104 times the scale of weak interactions. 1.1 The ISS Model Intriligator, Shih and Seiberg (ISS)[1] discovered susy breaking in a surprising context: a vectorlike theory, in which the Witten index was known to be non-zero. Their model is just SUSY QCD, with Nf > N + 1, and massive quarks. Such theories were thought not to break supersymmetry because: 1. The Witten index, ∆ = N . 2. In the limit of large mass, this theory reduces to a pure, SUSY gauge theory, which is known not to break susy. For many questions, holomorphy of quantities such as the superpotential is enough to insure that there are supersymmetric minima. Ironically, such gauge theories were originally proposed (with vanishing quark masses) as models of dynamical supersymmetry breaking; Witten’s computation of the index was viewed as clinching the case that such theories did not break supersymmetry. The breaking of supersymmetry is readily understood by considering the theory in its magnetic phase. In the infrared, the massless theory is described by an SU(Nf − N) gauge theory with Nf q and q̄ fields in the fundamental, and a set of “mesons”, Φff̄ . The theory has superpotential: W = q̄Φq. (1)