9 Supersymmetry breaking , R - symmetry , and conformal dynamics Yuji Omura

We study N = 1 global and local supersymmetric theories with a continuous global U(1)R symmetry. We discuss conditions for supersymmetry (SUSY) breaking and vacuum structures of R-symmetric SUSY models. Especially we find the conditions for R-symmetry breaking and runway vacua in global supersymmetric theories. We introduce explicit R-symmetry breaking terms into such models in global and local supersymmetric theories. Such explicit R-symmetry breaking terms can lead to a SUSY preserving minimum. We classify explicit R-symmetry breaking terms by the structure of newly appeared SUSY stationary points as a consequence of the R-breaking effect, which could make the SUSY breaking vacuum metastable. Based on the generic argument, we propose the scenario that conformal dynamics causes approximate R-symmetry and metastable SUSY breaking vacua. At a high energy scale, the superpotential in our model is not R-symmetric, and has a supersymmetric minimum. However, conformal dynamics suppresses several operators along the renormalization group (RG) flow toward the infrared fixed point. Then we can find an approximately R-symmetric superpotential, which has a metastable SUSY breaking vacuum, and the supersymmetric vacuum moves far away from the metastable supersymmetry breaking vacuum. Furthermore, we find that conformal dynamics also leads approximate R-symmetry in softly SUSY breaking theories, even in more complicated models such as the duality cascade. We investigate the RG flow of SUSY breaking terms as well as supersymmetric couplings in the duality cascade of softly broken supersymmetric theories. It is found that the magnitudes of SUSY breaking terms are suppressed in most regimes of the RG flow through the duality cascade and approximate R-symmetry is realized at a low energy scale. We also show the possibility that cascading would be terminated by the gauge symmetry breaking, which is induced by the so-called B-term. Finally, we find some models to arrive at standardmodel-like models and to cause gauge symmetry breaking corresponding to electro-weak symmetry breaking.