$SO(32)$ heterotic standard model vacua in general Calabi-Yau compactifications

TL;DR

This paper explores a flux breaking approach in $SO(32)$ heterotic string theory on Calabi-Yau threefolds, deriving Standard Model-like spectra with three generations and no chiral exotics, including a concrete example.

Contribution

It introduces a general formula for three-generation Standard Models in heterotic string theory with flux breaking, applicable to general Calabi-Yau compactifications.

Findings

Derived a formula for three generations without chiral exotics.

Constructed a concrete three-generation model on a specific Calabi-Yau.

Demonstrated background independence in the flux breaking scenario.

Abstract

We study a direct flux breaking scenario in $SO(32)$ heterotic string theory on general Calabi-Yau threefolds. The direct flux breaking, corresponding to hypercharge flux breaking in the F-theory context, allows us to derive the Standard Model in general Calabi-Yau compactifications. We present a general formula leading to the three generations of quarks and leptons and no chiral exotics in a background-independent way. As a concrete example, we show the three-generation model on a complete intersection Calabi-Yau threefold.