Hypercharge Flux in Heterotic Compactifications

TL;DR

This paper investigates heterotic Calabi-Yau models with hypercharge flux breaking, classifies possible embeddings, and proves a no-go theorem for most cases due to geometric and bundle constraints.

Contribution

It classifies hypercharge embeddings in heterotic models and establishes a no-go theorem limiting realistic model construction without GUT intermediates.

Findings

Classified hypercharge embeddings compatible with gauge unification.

Proved a no-go theorem for most embeddings preventing standard model spectra.

Identified the unique embedding that can potentially yield realistic models.

Abstract

We study heterotic Calabi-Yau models with hypercharge flux breaking, where the visible E8 gauge group is directly broken to the standard model group by a non-flat gauge bundle, rather than by a two-step process involving an intermediate grand unified theory and a Wilson line. It is shown that the required alternative E8 embeddings of hypercharge, normalized as required for gauge unification, can be found and we classify these possibilities. However, for all but one of these embeddings we prove a general no-go theorem which asserts that no suitable geometry and vector bundle leading to a standard model spectrum can be found. Intuitively, this happens due to the large number of index conditions which have to be imposed in order to obtain a correct physical spectrum in the absence of an underlying grand unified theory.