Yukawa Textures with Enhanced Symmetries in Heterotic Calabi-Yau Compactifications

TL;DR

This paper investigates the structure of Yukawa couplings in heterotic string compactifications, revealing unique textures and emergent flavor symmetries that influence quark mass patterns.

Contribution

It demonstrates that Calabi-Yau topology induces Yukawa textures beyond group symmetries and identifies emergent $U(2)$ flavor symmetry in moduli space affecting fermion masses.

Findings

Yukawa textures are determined by Calabi-Yau topology, not just symmetries.

A $U(2)$ flavor symmetry emerges at specific moduli space loci.

Perturbations around these loci produce realistic quark mass and mixing patterns.

Abstract

We clarify the structure of Yukawa couplings and mass matrices for matter fields in heterotic string theory on smooth Calabi-Yau threefolds with standard embedding. The topological structure of Calabi-Yau threefolds leads to interesting Yukawa textures that cannot be derived from group-theoretical symmetries, e.g., the so-called Weinberg texture in the case of two generations of matter fields. Furthermore, we find that a $U(2)$ flavor symmetry, which plays an important role in controlling higher-dimensional operators in the Standard Model effective field theory, emerges at specific loci in the moduli space of multi-Higgs fields. Small perturbations around these loci generate semi-realistic patterns of quark masses and mixings.