Stability of the Minimal Heterotic Standard Model Bundle
  The observable sector of the "minimal heterotic standard model" has precisely the matter spectrum of the MSSM: three families of quarks and leptons, each with a right-handed neutrino, and one Higgs-Higgs conjugate pair. In this paper, it is explicitly proven that the SU(4) holomorphic vector bundle leading to the MSSM spectrum in the observable sector is slope-stable. 
Volker Braun, Yang-Hui He, Burt A. Ovrut