Abstract
Some Calabi-Yau manifolds leading to three generations of chiral fermions in the heterotic E8×E8 some superstring theory are endowed with a freely acting discrete symmetry Z3, which when mapped homomorphically into the E6 subgroup of the first E8 causes it to break to ( SU (3))3 or SU(6)×U(1). The same discrete group can be mapped homomorphically into the second E8 and can result in its breaking. We obtain some of the maximal subgroups of E8 and present the breaking directions in weight space for some breakings. Flux-tubes arise in these theories and their significance in cosmology is briefly discussed.
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