TYPE II SUPERSTRINGS ON TWISTED GROUP MANIFOLDS AND THEIR HETEROTIC COUNTERPARTS

We construct Type II superstrings in four space-time dimensions compactified on a twisted Wess-Zumino-Witten model based on the group SU(2)3. It is shown that within this framework, it is possible to obtain models with N=6, 5 and 3 space-time supersymmetries, in addition to the usual models with N=8, 4 and 2. The map of these models into the corresponding heterotic superstrings with N=4, 2 and 1 space-time supersymmetries is also derived: in complete analogy to the compactifications on six-dimensional manifolds also in this case this map from Type II to heterotic superstrings corresponds geometrically to the embedding of the 9-dimensional compact manifold spin-connection into the gauge connection. The superstring compactifications we discussed are equivalent to asymmetric orbifold constructions in six-dimensions with no necessity, however, of introducing chiral bosons.