HETEROTIC SUPERSTRING VACUA IN 4 DIMENSIONS BASED ON NONCOMPACT AFFINE CURRENT-ALGEBRAS

New classes of unitary conformal and superconformal theories based on cosets of affine non-compact current algebras are suggested. Unitarity restrictions and the structure of the modules labelled by the primary states are discussed in general terms as well as in detail for SU(1,1)/U(1), SU(N,M)/SU(N) × SU(M) × U(1) and SL(2,C)/SU(2). Large classes of new N = 2 superconformal theories are classified and their central charges computed. This gives the non-compact counterpart of the Kazama-Suzuki models. It is shown that compact group and non-compact group Kazama-Suzuki models can be rewritten as coset models of the form (G × H)/H, where H is a maximal compact subgroup of G and G/H is kählerian. This reveals new symmetry structures which are useful in computations. It is shown that, in applications to heterotic superstring model building in four dimensions, a c ≤ 9 compact space can be constructed only from two non-compact N = 2 super-affine cosets based on SU(1,1)- k ̂ with k ̂ ≥ 3 and SU(2,1)- k ̂ with k ̂ ≥ 9. After performing a GSO projection and heterotic conversion à la Gepner, the massless spectrum of the c = 9 SU(1,1)-3 case is analysed in detail. With some simplifying assumptions on modular invariants it is outlined how the number of families would be computed. © 1990.