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arXiv · hep-th/0303020

Invariant Homology on Standard Model Manifolds

Burt A. Ovrut·Tony Pantev·Rene Reinbacher
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Abstract

Torus-fibered Calabi-Yau threefolds Z, with base dP_9 and fundamental group pi_1(Z)=Z_2 X Z_2, are reviewed. It is shown that Z=X/(Z_2 X Z_2), where X=B X_{P_1} B' are elliptically fibered Calabi-Yau threefolds that admit a freely acting Z_2 X Z_2 automorphism group. B and B' are rational elliptic surfaces, each with a Z_2 X Z_2 group of automorphisms. It is shown that the Z_2 X Z_2 invariant classes of curves of each surface have four generators which produce, via the fiber product, seven Z_2 X Z_2 invariant generators in H_4(X,Z). All invariant homology classes are computed explicitly. These descend to produce a rank seven homology group H_4(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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Burt A. Ovrut, Tony Pantev, Rene Reinbacher. 2003-03-04. Invariant Homology on Standard Model Manifolds. https://doi.org/10.1088/1126-6708%2F2004%2F01%2F059

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