Invariant Homology on Standard Model Manifolds
Abstract
Torus-fibered Calabi-Yau threefolds Z, with base dP9 and fundamental group pi1(Z)=Z2 X Z2, are reviewed. It is shown that Z=X/(Z2 X Z2), where X=B XP1 B' are elliptically fibered Calabi-Yau threefolds that admit a freely acting Z2 X Z2 automorphism group. B and B' are rational elliptic surfaces, each with a Z2 X Z2 group of automorphisms. It is shown that the Z2 X Z2 invariant classes of curves of each surface have four generators which produce, via the fiber product, seven Z2 X Z2 invariant generators in H4(X,Z). All invariant homology classes are computed explicitly. These descend to produce a rank seven homology group H4(Z,Z) on Z. The existence of these homology classes on Z is essential to the construction of anomaly free, three family standard-like models with suppressed nucleon decay in both weakly and strongly coupled heterotic superstring theory.
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