Abstract
Compactification of the field-theory limit of the E8 × E′8 heterotic string on six-dimensional coset manifolds is discussed, with specific reference to maintaining four-dimensional super-symmetry. By choosing a torsion proportional to the background value of the three-index field Hmnp occurring in the theory it is possible to satisfy the condition of SU(3) holonomy necessary for supersymmetry. However, in all cases considered, it is found impossible to satisfy all the remaining conditions for supersymmetry. If gaugino condensation is assumed to occur, it is possible to preserve supersymmetry satisfying all the modified requirements of supersymmetry for the spaces SU (3)/ U (1) × U (1), G 2/ SU (3) and SO (5)/ SU (2) × U (1). The question of chiral fermions is examined in these cases using the Atiyah-Singer index theorem. Background gauge fields, which correspond to different numbers of generations of chiral fermions, are constructed explicitly. In all these cases the low-energy symmetry group is E6 × E′8.
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