Supersymmetry Breaking Through Confining and Dual Theory Gauge Dynamics 1

We show that theories in the confining, free magnetic, and conformal phases can break supersymmetry through dynamical effects. To illustrate this, we present theories based on the gauge groups SU(n) × SU(4) × U(1) and SU(n) × SU(5) × U(1) with the field content obtained by decomposing an SU(m) theory with an antisymmetric tensor and m− 4 antifundamentals. Supported in part by DOE under cooperative agreement #DE-FC02-94ER40818 and #DE-FG05-90ER40599. NSF Young Investigator Award, Alfred P. Sloan Foundation Fellowship, DOE Outstanding Junior Investigator Award. Recently, there has been a dramatic increase in the number of dynamical supersymmetry breaking models [1, 2, 3, 4, 5]. In part this increase has been due to new methods for analyzing supersymmetric theories [6, 7]. While many of the first models for breaking supersymmetry had instanton or gaugino generated terms which kept fields away from the origin [1, 2, 8], recent work has argued that models in other phases can also break supersymmetry. In Ref. [4], it was argued that supersymmetry can be broken due to confinement. A nontrivial modification of the Kähler potential near the origin removes the supersymmetry preserving minimum. Alternatively, models with a quantum modified moduli space can also break supersymmetry [3] because the supersymmetry preserving origin is removed by the quantum modified constraint. Models in the conformal or free magnetic phase can also break supersymmetry. In the models which have been studied to now, these models broke supersymmetry through an O’Raifeartaigh mechanism in the dual theory [9, 10] or strong dynamics in the electric theory. A class of models described below is distinguished by the fact that the dynamics can be understood only in the dual description where dynamical effects are responsible for supersymmetry breaking. In a recent paper [5], a new class of models was studied which were based on a product group in which supersymmetry is broken dynamically. There it was argued that supersymmetry breaking could be understood as a collusion between separate dynamical effects from the two nonabelian gauge groups. In the first example, the 4-3-1 model based on the gauge group SU(4) × SU(3) × U(1), the exact superpotential could be found and the model was an O’Raifeartaigh model with both groups contributing to the final form of the superpotential. In all cases, supersymmetry breaking could be understood by taking a limit in which the gauge coupling of a confining gauge group is the biggest coupling. In this limit, Yukawa couplings which were necessary to lift flat directions turn into mass terms. Many flavors can be integrated out and the gauge dynamics of the second nonabelian gauge factor generated a superpotential which drives fields from the origin leading to the breaking of supersymmetry. In the particular models considered in Ref. [5], other mechanisms of supersymmetry breaking could appear as well in the limit that one of the gauge couplings dominated. For example, in the particular case of the 4-3-1 model supersymmetry breaking occurs in the strong Λ3 limit through confinement, analogous to the mechanism of Ref. [4]. On the other hand, if some of