The MSSM Spectrum from (0,2)-Deformations of the Heterotic Standard Embedding

TL;DR

This paper constructs heterotic string compactifications that precisely reproduce the MSSM spectrum by deforming standard embeddings on a specific Calabi-Yau threefold, achieving realistic particle physics models.

Contribution

It demonstrates the realization of MSSM spectrum in heterotic string theory through (0,2)-deformations of the standard embedding on a Calabi-Yau with specific properties.

Findings

Exact MSSM spectrum achieved in heterotic compactifications.

Stable bundles found on multiple moduli space branches.

Gauge symmetry broken to Standard Model via Wilson lines and deformations.

Abstract

We construct supersymmetric compactifications of E_8 \times E_8 heterotic string theory which realise exactly the massless spectrum of the Minimal Supersymmetric Standard Model (MSSM) at low energies. The starting point is the standard embedding on a Calabi-Yau threefold which has Hodge numbers (h^11,h^21) = (1,4) and fundamental group Z_12, which gives an E_6 grand unified theory with three net chiral generations. The gauge symmetry is then broken to that of the standard model by a combination of discrete Wilson lines and continuous deformation of the gauge bundle. On eight distinct branches of the moduli space, we find stable bundles with appropriate cohomology groups to give exactly the massless spectrum of the MSSM.