Symmetry breaking in three-generation Calabi-Yau manifolds

The spontaneous breaking of [SU(3)${]}^3$ symmetry to SU(3)×SU(2)×U(1) due to nonrenormalizable interactions in the three-generation Calabi-Yau superstring model is considered. It is seen that these models lead naturally to intermediate scales $M_I$∼${10}^{15}$ GeV with simultaneous formation of N and ${\nu }^c$ vacuum expectation values (VEV’s). The lowest-lying extrema automatically preserve matter parity and hence protect the model against too rapid proton decay. Models with matter parity also protect against electroweak Higgs VEV’s from forming at $M_I$. The intermediate mass scale produces some particles with mass O($M_I$). It also implies the existence of others with mass ∼1 TeV, which are possibly accessible to low-energy experiments.