Holomorphic Yukawa Couplings for Complete Intersection Calabi-Yau Manifolds

TL;DR

This paper introduces new methods to compute holomorphic Yukawa couplings in heterotic string compactifications on complete intersection Calabi-Yau manifolds, extending previous techniques and providing explicit calculations for realistic models.

Contribution

It develops explicit construction techniques for bundle-valued forms and relates them to algebraic methods, including a vanishing theorem for certain Yukawa couplings.

Findings

Derived explicit formulas for Yukawa couplings on complete intersection Calabi-Yau manifolds.

Established a vanishing theorem explaining zero Yukawa couplings due to topological reasons.

Calculated Yukawa couplings for SU(5) models on specific manifolds.

Abstract

We develop methods to compute holomorphic Yukawa couplings for heterotic compactifications on complete intersection Calabi-Yau manifolds, generalising results of an earlier paper for Calabi-Yau hypersurfaces. Our methods are based on constructing the required bundle-valued forms explicitly and evaluating the relevant integrals over the projective ambient space. We also show how our approach relates to an earlier, algebraic one to calculate the holomorphic Yukawa couplings. A vanishing theorem, which we prove, implies that certain Yukawa couplings allowed by low-energy symmetries are zero due to topological reasons. To illustrate our methods, we calculate Yukawa couplings for SU(5)-based standard models on a co-dimension two complete intersection manifold.