Yukawa Textures From Heterotic Stability Walls

TL;DR

This paper explores how stability walls in heterotic string compactifications impose constraints on Yukawa couplings, leading to hierarchical textures and potential explanations for fermion mass patterns.

Contribution

It demonstrates that stability walls induce extended U(1) symmetries which strongly restrict superpotential terms, resulting in specific Yukawa textures and mass hierarchies.

Findings

Yukawa textures exhibit hierarchical structures with large couplings on the wall

Suppressed interactions can grow off the wall as U(1) symmetries break

Explicit examples include models with three families and no vector-like pairs

Abstract

A holomorphic vector bundle on a Calabi-Yau threefold, X, with h^{1,1}(X)>1 can have regions of its Kahler cone where it is slope-stable, that is, where the four-dimensional theory is N=1 supersymmetric, bounded by "walls of stability". On these walls the bundle becomes poly-stable, decomposing into a direct sum, and the low energy gauge group is enhanced by at least one anomalous U(1) gauge factor. In this paper, we show that these additional symmetries can strongly constrain the superpotential in the stable region, leading to non-trivial textures of Yukawa interactions and restrictions on allowed masses for vector-like pairs of matter multiplets. The Yukawa textures exhibit a hierarchy; large couplings arise on the stability wall and some suppressed interactions "grow back" off the wall, where the extended U(1) symmetries are spontaneously broken. A number of explicit examples are presented involving both one and two stability walls, with different decompositions of the bundle structure group. A three family standard-like model with no vector-like pairs is given as an example of a class of SU(4) bundles that has a naturally heavy third quark/lepton family. Finally, we present the complete set of Yukawa textures that can arise for any holomorphic bundle with one stability wall where the structure group breaks into two factors.