The Family Problem: Hints from Heterotic Line Bundle Models

Understand

Within the class of heterotic line bundle models, we argue that N=1 vacua which lead to a small number of low-energy chiral families are preferred.

• By imposing an upper limit on the volume of the internal manifold, as required in order to obtain finite values of the four-dimensional gauge couplings, and validity of the supergravity approximation we show that, for a given manifold, only a finite number of line bundle sums are consistent with supersymmetry.
• By explicitly scanning over this finite set of line bundle models on certain manifolds we show that, for a sufficiently small volume of the internal manifold, the family number distribution peaks at small values, consistent with three chiral families.
• The relation between the maximal number of families and the gauge coupling is discussed, which hints towards a possible explanation of the family problem.