Yukawa Textures From Singular Spectral Data

TL;DR

This paper uses singular spectral data to analyze Yukawa textures in heterotic models, revealing detailed cohomology structures and their relation to F-theory, with potential for broader application to elliptic Calabi-Yau manifolds.

Contribution

It introduces a novel spectral data approach to dissect Yukawa textures and connect heterotic and F-theory models, applicable to Weierstrass elliptic fibrations.

Findings

Cohomologies can be decomposed into smaller, analyzable parts.

Identification of zero mode containing pieces in cohomologies.

Manifest relationship established between heterotic Yukawa textures and F-theory fields.

Abstract

The Yukawa textures of effective heterotic models are studied by using singular spectral data. One advantage of this approach is that it is possible to dissect the cohomologies of the bundles into smaller parts and identify the pieces that contain the zero modes, which can potentially have non-zero Yukawa couplings. Another advantage is the manifest relationship between the Yukawa textures in heterotic models and local F-theory models in terms of fields living in bulk or localized inside the 7-branes. We only work with Weierstrass elliptically fibered Calabi-Yau manifolds here. The idea for generalizing this approach to every elliptically fibered Calabi-Yau with rational sections is given at the end of this paper.