Elliptic Calabi-Yau threefolds with ℤ3 × ℤ3 Wilson lines

Abstract

A torus fibered Calabi-Yau threefold with first homotopy group ℤ3 × ℤ3 is constructed as a free quotient of a fiber product of two dP9 surfaces. Calabi-Yau threefolds of this type admit ℤ3 × ℤ3 Wilson lines. In conjunction with SU(4) holomorphic vector bundles, such vacua lead to anomaly free, three generation models of particle physics with a right handed neutrino and a U(1)B-L gauge factor, in addition to the SU(3)C × SU(2)L × U(1)Y standard model gauge group. This factor helps to naturally suppress nucleon decay. The moduli space and Dolbeault cohomology of the threefold is also discussed. © SISSA/ISAS 2005.