Superconformal Minimal Models and Their Role in Superstring Compactification

To summarize, the organization of this work is as follows. The remaining part of this chapter deals with the basic aspects of the conformal field theories and it is useful to fix the notation. Chapter 2 is devoted to the N =1 superconformal formalism: we skip the NS sector (for a general discussion we refer to [16) and the papers listed under it) and we concentrate on the problem of the description of the R sector, which is original part. Using our construction of the R vertices and analysing the singularities of the correlators we carry out explicit computations of the correlation functions and we extract the structure constants of the theory. In chapter 3 we present a complete study of the N =2 m.m. with central charge c <= 3 we compute many correlators and the FR's. The most important original result is the discovery of the Zp+2 symmetry present in the N =2 m.m. Finally, in the chapter 4 we face the problem of compactification of heteroric string. After a general discussion on the subject, by using the Gepner's approach we construct the internal compactified space by N =2 m.m.; in particular we analyse the four and three generation case and give the allowed Yukawa couplings. Finally, Appendix A is devoted to the monodromy properties of the simplest solutions of the Ramond correlators in N=l superconformal nl.ln., Appendix B discusses the free fermionic systems and Appendix C deals with a brief introduction to the Calabi-Yau spaces.