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.
