Some current problems in particle physics beyond the standard model

In this thesis several problems are addressed in trying to extend particle physics beyond the standard model. In chapter 1, the cross section for fermions scattering from cosmic string solitons which are left from symmetry-breaking phase transitions in the early universe are computed, and the consequences for the possibility of observing the strings are discussed. In chapter 2, the form of the Wess-Zumino anomalous interaction term for the 2-dimensional supersymmetric nonlinear sigma-model was derived; 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, a mechanism for breaking supersymmetry in supersymmetric string theories is analyzed, which have the potential to provide unification of gauge interactions with gravity in a consistent quantum theory