Monad Bundles in Heterotic String Compactifications

TL;DR

This paper investigates positive monad vector bundles on Calabi-Yau manifolds for heterotic string compactifications, demonstrating finiteness, spectrum computation, and stability conditions, significantly narrowing viable models.

Contribution

It establishes the finiteness of such bundles, provides methods to compute particle spectra, and verifies necessary stability conditions, advancing the understanding of heterotic compactifications.

Findings

Approximately 7000 models satisfy the anomaly condition.

No vector-like pairs found in any models.

Physical constraints drastically reduce viable models.

Abstract

In this paper, we study positive monad vector bundles on complete intersection Calabi-Yau manifolds in the context of E8 x E8 heterotic string compactifications. We show that the class of such bundles, subject to the heterotic anomaly condition, is finite and consists of about 7000 models. We explain how to compute the complete particle spectrum for these models. In particular, we prove the absence of vector-like family anti-family pairs in all cases. We also verify a set of highly non-trivial necessary conditions for the stability of the bundles. A full stability proof will appear in a companion paper. A scan over all models shows that even a few rudimentary physical constraints reduces the number of viable models drastically.