Combinatorics in N = 1 Heterotic Vacua

TL;DR

This paper reviews an algorithmic approach to exploring heterotic string vacua on Calabi-Yau three-folds, emphasizing combinatorial methods for constructing vector bundles to identify Standard-like models.

Contribution

It introduces a combinatorial algorithmic strategy for systematically exploring heterotic vacua with vector bundles on Calabi-Yau hypersurfaces in toric varieties.

Findings

Developed an algorithmic framework for heterotic vacua exploration.

Applied combinatorial methods to construct vector bundles as monads.

Facilitated search for Standard-like heterotic models.

Abstract

We briefly review an algorithmic strategy to explore the landscape of heterotic E8 \times E8 vacua, in the context of compactifying smooth Calabi-Yau three-folds with vector bundles. The Calabi-Yau three-folds are algebraically realised as hypersurfaces in toric varieties and a large class of vector bundles are constructed thereon as monads. In the spirit of searching for Standard-like heterotic vacua, emphasis is placed on the integer combinatorics of the model-building programme.