UC San Diego

There are two basic topics investigated is this dissertation. The first has to do with the symmetries of superconformal field theories (SCFTs). A general constraint that, in principle, determines the superconformal U(1)R symmetry of 4d N=1 SCFTs and 3d N=2 SCFTs is identified. Among all possibilities, the superconformal U(1)RR is that which minimizes the coefficient, \[tau\]RR, of its two-point function. For 4d N=1 SCFTs, \[tau\]RR-minimization gives an alternative to a- maximization. \[tau\]RR-minimization also applies in 3d, where no condition for determining the superconformal U(1)RR had been known. The second general topic discussed is supersymmetry breaking. Three chapters are devoted to this topic. In the first, the gauge sector of ordinary gauge mediation is generalized. The two-loop calculation of sfermion masses is generalized to allow for an arbitrary gauge group with an arbitrary supersymmetric Higgsing. The generic effect on the MSSM spectrum from additional Higgsed gauge structure is to increase the sfermion masses relative to the gaugino masses. The subsequent chapter deals with "general gauge mediation," in which the hidden-sector effects are expressed in terms of current two-point functions. The previously discussed generalization of the gauge sector to allow for Higgsing is computed in this formalism. The effective potential for squark pseudo-D-flat directions is also given. This reduces to the sfermion soft masses near the origin, and the full potential, away from the origin, can be useful for cosmological applications. The results are then analyzed in the limit of small supersymmetry breaking. In the final chapter, pseudomoduli, which determine whether or not supersymmetry is broken, are studied. Types of pseudomoduli that arise when supersymmetry is dynamically broken in infrared-free low-energy theories are classified. It is shown that, even if the pseudomoduli potential is generated at higher loops, there is a regime where the potential can be determined from one-loop running data. In this regime, we compute whether the potential for various types of pseudomoduli is safe, has a dangerous runaway to the UV cutoff, or is incalculable.