Some Current Problems in Particle Physics Beyond the Standard Model

In this thesis I address several problems in trying to extend particle physics beyond the standard model. In chapter 1, I compute the cross section for fermions scattering from cosmic string solitons which are left from symmetry -breaking phase transitions in the early universe, and discuss the consequences for the possibility of observing the strings. In chapter 2, I derive the form of the Wess-Zumino anomalous interaction term for the 2-dimensional supersymmetric nonlinear sigma-model; in chapter 3, a similar technique is applied to the 4-dimensional supersymmetric nonlinear sigma-model, and constraints are obtained on the form of low-energy effective actions of supersymmetric gauge theories. In particular, it is shown that sigma-models on compact manifolds cannot have a Wess-Zumino interaction with unbroken supersymmetry. In chapter 4, I analyze a mechanism for breaking supersymmetry in supersymmetric string theories, which have the potential to provide unification of gauge interactions with gravity in a consistent quantum theory.