Torus-Fibered Calabi-Yau Threefolds with Non-Trivial Fundamental Group
Abstract
We construct smooth Calabi-Yau threefolds Z, torus-fibered over a dP9 base, with fundamental group Z2 X Z2. To do this, the structure of rational elliptic surfaces is studied and it is shown that a restricted subset of such surfaces admit at least a Z2 X Z2 group of automorphisms. One then constructs Calabi-Yau threefolds X as the fiber product of two such dP9 surfaces, demonstrating that the involutions on the surfaces lift to a freely acting Z2 X Z2 group of automorphisms on X. The threefolds Z are then obtained as the quotient Z=X/(Z2 X Z2). These Calabi-Yau spaces Z admit stable, holomorphic SU(4) vector bundles which, in conjunction with Z2 X Z2 Wilson lines, lead to standard-like models of particle physics with naturally suppressed nucleon decay.
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