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Exploring positive monad bundles and a new heterotic standard model. (English) Zbl 1270.81146
Summary: A complete analysis of all heterotic Calabi-Yau compactifications based on positive two-term monad bundles over favourable complete intersection Calabi-Yau threefolds is performed. We show that the original data set of about 7000 models contains 91 standard-like models which we describe in detail. A closer analysis of Wilson-line breaking for these models reveals that none of them gives rise to precisely the matter field content of the standard model. We conclude that the entire set of positive two-term monads on complete intersection Calabi-Yau manifolds is ruled out on phenomenological grounds. We also take a first step in analyzing the larger class of non-positive monads. In particular, we construct a supersymmetric heterotic standard model within this class. This model has the standard model gauge group and an additional \(\text{U}(1)_{B-L}\) symmetry, precisely three families of quarks and leptons, one pair of Higgs doublets and no anti-families or exotics of any kind.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81V22 Unified quantum theories
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
Software:
Macaulay2; SINGULAR
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