Holomorphic Yukawa Couplings in Heterotic String Theory

TL;DR

This paper introduces differential geometric techniques to compute holomorphic Yukawa couplings in heterotic string models on Calabi-Yau manifolds, relating them to algebraic methods and analyzing their behavior across moduli space.

Contribution

It develops new differential geometric methods for calculating Yukawa couplings in heterotic models and relates these to existing algebraic approaches.

Findings

Yukawa couplings depend on complex structure moduli.

Yukawa matrix rank can decrease at specific moduli.

Explicit calculations for standard model Yukawa couplings.

Abstract

We develop techniques, based on differential geometry, to compute holomorphic Yukawa couplings for heterotic line bundle models on Calabi-Yau manifolds defined as complete intersections in projective spaces. It is shown explicitly how these techniques relate to algebraic methods for computing holomorphic Yukawa couplings. We apply our methods to various examples and evaluate the holomorphic Yukawa couplings explicitly as functions of the complex structure moduli. It is shown that the rank of the Yukawa matrix can decrease at specific loci in complex structure moduli space. In particular, we compute the up Yukawa coupling and the singlet-Higgs-lepton trilinear coupling in the heterotic standard model described in arXiv:1404.2767