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A heterotic standard model. (English) Zbl 1247.81349
Summary: Within the context of the \(E_8\times E_8\) heterotic superstring compactified on a smooth Calabi-Yau threefold with an \(\mathrm{SU}(4)\) gauge instanton, we show the existence of simple, realistic \(N=1\) supersymmetric vacua that are compatible with low-energy particle physics. The observable sector of these vacua has gauge group \(\mathrm{SU}(3)_C\times\mathrm{SU}(2)_L\times\mathrm{U}(1)_Y\times\mathrm{U}(1)_{B-L}\), three families of quarks and leptons, each with an additional right-handed neutrino, two Higgs-Higgs conjugate pairs, a small number of uncharged moduli and no exotic matter. The hidden sector contains non-abelian gauge fields and moduli. In the strong coupling case there is no exotic matter, whereas for weak coupling there are a small number of additional matter multiplets in the hidden sector. The construction exploits a mechanism for ‘splitting’ multiplets. The minimal nature and rarity of these vacua suggest the possible theoretical and experimental relevance of spontaneously broken \(\mathrm{U}(1)_{B-L}\) gauge symmetry and two Higgs-Higgs conjugate pairs. The \(\mathrm{U}(1)_{B-L}\) symmetry helps to naturally suppress the rate of nucleon decay.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81V22 Unified quantum theories
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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