The MSSM spectrum from (0,2)-deformations of the heterotic standard embedding

Abstract

We construct supersymmetric compactifications of E 8×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 1,1, h 2,1) = (1, 4) and fundamental group $ {\mathbb{Z}_{{12}}} $ , which gives an E 6 grand unified theory with three net chiral generations. The gauge sym- metry 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.