Exploring a new peak in the heterotic landscape

TL;DR

This paper investigates the existence of realistic heterotic string vacua on a specific Calabi-Yau threefold, establishing a no-go theorem that rules out certain stable vector bundles under mild assumptions.

Contribution

It introduces a no-go theorem for stable holomorphic vector bundles on a new Abelian surface fibered Calabi-Yau threefold, advancing understanding of heterotic vacua constraints.

Findings

No stable holomorphic vector bundles satisfy the constraints on the studied manifold.

Fourier-Mukai transform analysis is crucial for understanding vector bundle properties.

The results impose limitations on heterotic string model building on this class of manifolds.

Abstract

We study the existence of realistic heterotic vacua on a new Abelian surface fibered Calabi-Yau threefold X with Z_8 x Z_8 fundamental group. Our main result is a no-go theorem, which says that (under mild assumptions) there is no stable holomorphic vector bundle on X satisfying the constraints required by global consistency of the heterotic vacuum and phenomenology. To prove the theorem we explore in some detail the Fourier-Mukai transform of vector bundles on Abelian surface fibrations.