Exploring Positive Monad Bundles And A New Heterotic Standard Model

TL;DR

The authors perform a comprehensive survey of positive two-term monad bundles on favourable CICYs to identify heterotic vacua with three chiral generations, finding 91 viable candidates but ruling them out phenomenologically after standard GUT breaking by Wilson lines. They develop a robust framework for analyzing equivariant structures and the downstairs spectra, showing that most positive monads fail to descend or yield MSSM-like content, and they illustrate the need to explore non-positive monads. As a proof of concept beyond the positive subset, they construct a semi-positive, rank‑4 monad on a bi‑cubic Calabi–Yau that, with a carefully chosen $\mathbb{Z}_3\times\mathbb{Z}_3$ equivariant structure and Wilson lines, yields a supersymmetric $SO(10)$ heterotic standard model with gauge group $SU(3)\times SU(2)\times U(1)_Y\times U(1)_{B-L}$, three generations, three right-handed neutrinos, and, at a special locus, a single Higgs doublet pair and no exotics. Overall, the work demonstrates both the limitations of the positive monad class and the viability of broader monad constructions for realistic string vacua, while laying out concrete tools for systematic future searches.

Abstract

A complete analysis of all heterotic Calabi-Yau compactifications based on positive two-term monad bundles over favourable complete intersection Calabi-Yau threefolds is performed. We show that the original data set of about 7000 models contains 91 standard-like models which we describe in detail. A closer analysis of Wilson-line breaking for these models reveals that none of them gives rise to precisely the matter field content of the standard model. We conclude that the entire set of positive two-term monads on complete intersection Calabi-Yau manifolds is ruled out on phenomenological grounds. We also take a first step in analyzing the larger class of non-positive monads. In particular, we construct a supersymmetric heterotic standard model within this class. This model has the standard model gauge group and an additional U(1)_{B-L} symmetry, precisely three families of quarks and leptons, one pair of Higgs doublets and no anti-families or exotics of any kind.