A Three-Generation Calabi-Yau Manifold with Small Hodge Numbers

Understand

We present a complete intersection Calabi-Yau manifold Y that has Euler number -72 and which admits free actions by two groups of automorphisms of order 12.

• These are the cyclic group Z_12 and the non-Abelian dicyclic group Dic_3.
• The quotient manifolds have chi=-6 and Hodge numbers (h^11,h^21)=(1,4).
• With the standard embedding of the spin connection in the gauge group, Y gives rise to an E_6 gauge theory with 3 chiral generations of particles.