Dynamical supersymmetry breaking in a long-lived meta-stable vacuum is a phenomenologically viable possibility. This relatively unexplored avenue leads to many new models of dynamical supersymmetry breaking. Here, we present a surprisingly simple class of models with meta-stable dynamical supersymmetry breaking: N = 1 supersymmetric QCD, with massive flavors. Though these theories are strongly coupled, we definitively demonstrate the existence of meta-stable vacua by using the free-magnetic dual. Model building challenges, such as large flavor symmetries and the absence of an R-symmetry, are easily accommodated in these theories. Their simplicity also suggests that broken supersymmetry is generic in supersymmetric field theory and in the landscape of string vacua.

We discuss non-trivial fixed points of the renormalization group with dual descriptions in N = 4 gauge theories in three dimensions. This new duality acts as mirror symmetry, exchanging the Higgs and Coulomb branches of the theories. Quantum effects on the Coulomb branch arise classically on the Higgs branch of the dual theory. We present examples of dual theories whose Higgs/Coulomb branch are the ALE spaces and whose Coulomb/Higgs branches are the moduli space of instantons of the corresponding ADE gauge group. In particular, we show that in three dimensions small E 8 instantons in string theory are described by a local quantum field theory. 7/96

We discuss five-dimensional supersymmetric gauge theories. An anomaly renders some theories inconsistent and others consistent only upon including a Wess-Zumino type Chern-Simons term. We discuss some necessary conditions for existence of nontrivial renormalization group fixed points and find all possible gauge groups and matter content which satisfy them. In some cases, the existence of these fixed points can be inferred from string duality considerations. In other cases, they arise from M-theory on Calabi-Yau threefolds. We explore connections between aspects of the gauge theory and Calabi-Yau geometry. A consequence of our classification of field theories with nontrivial fixed points is a fairly complete classification of a class of singularities of Calabi-Yau threefolds which generalize the "del Pezzo contractions" and occur at higher codimension walls of the Kähler cone. 2/97

We consider general aspects of N = 2 gauge theories in three dimensions, including their multiplet structure, anomalies and non-renormalization theorems. For U (1) gauge theories, we discuss the quantum corrections to the moduli space, and their relation to "mirror symmetries" of 3d N = 4 theories. Mirror symmetry is given an interpretation in terms of vortices. For SU (N c ) gauge groups with N f fundamental flavors, we show that, depending on the number of flavors, there are quantum moduli spaces of vacua with various phenomena near the origin.3/97 * On leave

An exact and general solution is presented for a previously open problem. We show that the superconformal R-symmetry of any 4d SCFT is exactly and uniquely determined by a maximization principle: it is the R-symmetry, among all possibilities, which (locally) maximizes the combination of 't Hooft anomalies a trial (R) ≡ (9TrR 3 − 3TrR)/32. The maximal value of a trial is then, by a result of Anselmi et. al., the central charge a of the SCFT. Our a trial maximization principle almost immediately ensures that the central charge a decreases upon any RG flow, since relevant deformations force a trial to be maximized over a subset of the previously possible R-symmetries. Using a trial maximization, we find the exact superconformal R-symmetry (and thus the exact anomalous dimensions of all chiral operators) in a variety of previously mysterious 4d N = 1 SCFTs. As a check, we verify that our exact results reproduce the perturbative anomalous dimensions in all perturbatively accessible RG fixed points. Our result implies that N = 1 SCFTs are algebraic: the exact scaling dimensions of all chiral primary operators, and the central charges a and c, are always algebraic numbers.