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Moduli dependent spectra of heterotic compactifications. (English) Zbl 1247.14044
Summary: Explicit methods are presented for computing the cohomology of stable, holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds. The complete particle spectrum of the low-energy, four-dimensional theory is specified by the dimensions of specific cohomology groups. The spectrum is shown to depend on the choice of vector bundle moduli, jumping up from a generic minimal result to attain many higher values on subspaces of co-dimension one or higher in the moduli space. An explicit example is presented within the context of a heterotic vacuum corresponding to an \(SU(5)\) GUT in four dimensions.

MSC:
14J81 Relationships between surfaces, higher-dimensional varieties, and physics
83E30 String and superstring theories in gravitational theory
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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