String compactifications and N=2 superconformal coset constructions

We consider the class of string compactifications obtained through the tensoring of the N=2 superconformal theories recently constructed by Kazama and Suzuki. A classification of all c=9 and c=6 models obtained from N=2 theories based on hermitian symmetric spaces is given. The number of E₆ generations and antigenerations for c=9 models based on SU(m+1)/SU(m)×U(1) is also provided. A number of these models correspond to deformations of others previously obtained from tensoring of minimal N=2 theories as can be deduced from the corresponding Landau-Ginzburg superpotential. Many others are genuine new compactifications. It is also shown how more general modular invariant projections lead to new models both in the minimal and Kazama-Suzuki constructions. As an example, we obtain the standard Z₃-orbifold as a particular projection of the (k=1)⁹ Gepner model.