The Family Problem: Hints from Heterotic Line Bundle Models

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.

16 pages Latex

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Cited by in corpus (7)

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• Formulae for Line Bundle Cohomology on Calabi-Yau Threefolds
• Jumping Spectra and Vanishing Couplings in Heterotic Line Bundle Standard Models
• Matter Field Kahler Metric in Heterotic String Theory from Localisation
• Generalized Vanishing Theorems for Yukawa Couplings in Heterotic Compactifications
• Yukawa Unification in Heterotic String Theory
• Upper bound on the Atiyah-Singer index from tadpole cancellation