Extensions of the standard model

In these lectures we focus on several issues that arise in theoretical extensions of the standard model. First we describe the kinds of fermions that can be added to the standard model without affecting known phenomenology. We focus in particular on three types: the vector-like completion of the existing fermions as would be predicted by a Kaluza-Klein type theory, which we find cannot be realistically achieved without some chiral symmetry; fermions which are vector-like by themselves, such as do appear in supersymmetric extensions, and finally anomaly-free chiral sets of fermions. We note that a chiral symmetry, such as the Peccei-Quinn symmetry can be used to produce a vector-like theory which, at scales less than M/sub W/, appears to be chiral. Next, we turn to the analysis of the second hierarchy problem which arises in Grand Unified extensions of the standard model, and plays a crucial role in proton decay of supersymmetric extensions. We review the known mechanisms for avoiding this problem and present a new one which seems to lead to the (family) triplication of the gauge group. Finally, this being a summer school, we present a list of homework problems. 44 references