On Vector Bundles and Chiral Matter in N=1 Heterotic Compactifications

TL;DR

This paper calculates the number of chiral fermion generations in heterotic string compactifications on Calabi-Yau threefolds with specific SU(n) bundles, comparing different mathematical approaches and discussing implications for F-theory.

Contribution

It introduces a parabolic approach to determine chiral matter in heterotic compactifications and compares it with spectral cover methods.

Findings

Derived formulas for chiral fermion count using parabolic bundles.

Compared parabolic and spectral cover approaches for consistency.

Commented on the interpretation of net chiral number in F-theory.

Abstract

In this note we derive the net number of generations of chiral fermions in heterotic string compactifications on Calabi-Yau threefolds with certain SU(n) vector bundles, for n odd, using the parabolic approach for bundles. We compare our results with the spectral cover construction for bundles and make a comment on the net number interpretation in F-theory.