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The MSSM spectrum from \((0,2)\)-deformations of the heterotic standard embedding. (English) Zbl 1348.81435
Summary: 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 CalabiYau 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 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.

81T70 Quantization in field theory; cohomological methods
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
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