Yukawa Textures with Enhanced Symmetries in Heterotic Calabi-Yau Compactifications

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.

💡 Research Summary

The paper investigates the origin and structure of Yukawa couplings and fermion mass matrices in heterotic string theory compactified on smooth Calabi‑Yau (CY) three‑folds with the standard embedding. In this setting the ten‑dimensional gauge group E₈×E₈ is broken to E₆×E₈′, with the SU(3) bundle identified with the tangent bundle of the CY. Consequently, the 27 representation of E₆ (containing quarks, leptons and Higgs fields) is in one‑to‑one correspondence with the Kähler moduli, while the 27̅ corresponds to the complex‑structure moduli. The low‑energy effective action is therefore directly determined by the geometry of the CY: the Kähler potential for the matter fields is proportional to the Kähler potential of the Kähler moduli, and the holomorphic Yukawa couplings are given by the triple intersection numbers κ_{abc} of the CY three‑fold, \