The Family Problem: Hints from Heterotic Line Bundle Models

TL;DR

This paper investigates heterotic line bundle models and suggests that small internal manifold volume constraints favor vacua with a small number of chiral families, potentially explaining the family problem.

Contribution

It introduces a finite set of consistent line bundle models under volume and supergravity constraints and analyzes their family number distribution.

Findings

Family number distribution peaks at small values, consistent with three families.

Finite models are identified under volume and supersymmetry constraints.

Hints at a connection between maximal family number and gauge coupling.

Abstract

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.