(2, 2) VACUA OF THE HETEROTIC SUPERSTRING COMPACTIFIED ON SU(2)3 GROUPFOLDS

In this paper we classify the (2, 2) superstring vacua corresponding to non-linear sigma-models on SU(2)3 groupfolds fermionized by 18 + 18 Majorana fermions. For the subclass of the completely bosonizable vacua, the generation number 1/2-chi is a multiple of 12 and the number of tangent-bundle deformations End(T) is a multiple of 4. The dimensions of the moduli spaces h1,1, h2,1 are small odd numbers in the range 1 divided-by approximately 50. Very few of these vacua have the same Dolbeault cohomology as those described by minimal model tensor products, CICY, or Calabi-Yau threefolds in weighted P4. The vacua we classify are characterized by a rank 8 enhancement group and some of them can be viewed as N = 2 truncations. We also discuss examples of vacua that are only partially bosonizable, showing that the class of vacua obtained by free fermion constructions is not fully contained in the class of vacua obtained by lattice constructions.