Abstract (Elsevier)
A new class of unitary N =2 superconformal theories, including those with central charge > 3, is constructed via the coset space (G/H) method applied to super-Kac-Moody algebras. The relevant coset spaces of particular interest are the hermitian symmetric spaces. The theories based on them contain those with the Virasoro central charge equalling 9, the critical value for the internal part of a consistent superstring compactification. We show, following the method of Gepner, that it is possible to construct modular invariant four dimensional heterotic-type string theories with the gauge group E 8 × E 6 with no extra gauge groups.