Heterotic Compactification, An Algorithmic Approach

TL;DR

This paper introduces computational algebraic geometry techniques to analyze heterotic string compactifications, proving stability and calculating particle spectra on Calabi-Yau manifolds with positive monad bundles, revealing moduli-dependent spectra and no anti-generations.

Contribution

It provides new algorithmic methods for stability proofs and spectrum calculations in heterotic compactifications, focusing on complete intersection Calabi-Yau manifolds.

Findings

All studied bundles are stable.

Number of anti-generations vanishes.

Spectrum depends on moduli.

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.