Triadophilia: A Special Corner in the Landscape

Understand

It is well known that there are a great many apparently consistent vacua of string theory.

• We draw attention to the fact that there appear to be very few Calabi--Yau manifolds with the Hodge numbers h^{11} and h^{21} both small.
• Of these, the case (h^{11}, h^{21})=(3,3) corresponds to a manifold on which a three generation heterotic model has recently been constructed.
• We point out also that there is a very close relation between this manifold and several familiar manifolds including the `three-generation' manifolds with \chi=-6 that were found by Tian and Yau, and by Schimmrigk, during early investigations.