Heterotic Compactification, An Algorithmic Approach

TL;DR

The paper develops an algorithmic program to construct and analyze heterotic compactifications on complete intersection Calabi–Yau threefolds, by classifying positive monad bundles of rank $3$–$5$ and proving their stability via Hoppe’s criterion. It combines analytic methods with computer algebra (notably Macaulay2) to compute full low‑energy spectra, including singlets, across five CYs embedded in projective spaces. A key finding is the systematic absence of anti‑generations and a spectrum that depends on complex‑structure and bundle moduli, with a finite, enumerated set of $37$ models (plus extended counts if divisibility by 3 is not required). The work demonstrates that an algorithmic, data‑driven approach can effectively explore heterotic vacua near realistic phenomenology and sets the stage for larger-scale searches in broader CY classes.

Abstract

We approach string phenomenology from the perspective of computational algebraic geometry, by providing new and efficient techniques for proving stability and calculating particle spectra in heterotic compactifications. This is done in the context of complete intersection Calabi-Yau manifolds in a single projective space where we classify positive monad bundles. Using a combination of analytic methods and computer algebra we prove stability for all such bundles and compute the complete particle spectrum, including gauge singlets. In particular, we find that the number of anti-generations vanishes for all our bundles and that the spectrum is manifestly moduli-dependent.