Yukawa Couplings in Heterotic Standard Models

TL;DR

This work addresses the challenge of generating Yukawa couplings in realistic heterotic string vacua by formulating Yukawa terms as triple products of cohomology groups and exploiting two geometric Leray filtrations. The authors apply the formalism to the minimal heterotic standard model, demonstrating non-vanishing Yukawas with a constrained texture: only couplings involving the first family to the second and third survive due to a pair of (p,q) and [s,t] selection rules, and only one Higgs pair remains after Wilson line projection. Consequently, the leading-order mass matrix yields one massless generation and two nonzero masses of order the electroweak scale, with the exact values moduli-dependent and subject to higher-order or non-perturbative corrections. The construction provides a concrete mechanism to realize MSSM-like spectra with realistic Yukawa textures in heterotic compactifications and illustrates how geometry and bundle data control flavor structure in string-derived models.

Abstract

In this paper, we present a formalism for computing the Yukawa couplings in heterotic standard models. This is accomplished by calculating the relevant triple products of cohomology groups, leading to terms proportional to Q*H*u, Q*Hbar*d, L*H*nu and L*Hbar*e in the low energy superpotential. These interactions are subject to two very restrictive selection rules arising from the geometry of the Calabi-Yau manifold. We apply our formalism to the "minimal" heterotic standard model whose observable sector matter spectrum is exactly that of the MSSM. The non-vanishing Yukawa interactions are explicitly computed in this context. These interactions exhibit a texture rendering one out of the three quark/lepton families naturally light.