Abstract
We briefly review an algorithmic strategy to explore the landscape of heteroticE8×E8vacua, in the context of compactifying smooth Calabi-Yau threefolds with vector bundles. The Calabi-Yau threefolds are algebraically realised as hypersurfaces in toric varieties, and a large class of vector bundles are constructed thereon as monads. In the spirit of searching for standard-like heterotic vacua, emphasis is placed on the integer combinatorics of the model-building programme.
Highlights
Compactifications of E8 × E8 heterotic theory 1, 2 and heterotic M-theory 3–7 on smooth Calabi-Yau threefolds provide a simple and compelling way to reach N 1 supersymmetry at four dimensions
We have discussed a systematic approach towards standard-like heterotic vacua
Simplicity of the integer combinatorics for the N 1 heterotic vacua was the essential feature that made this approach a tractable programme. It was motivated by the general observation that any carefully chosen single model is likely to fail the detailed structure of the standard model
Summary
Compactifications of E8 × E8 heterotic theory 1, 2 and heterotic M-theory 3–7 on smooth Calabi-Yau threefolds provide a simple and compelling way to reach N 1 supersymmetry at four dimensions. The gauge field should satisfy the Hermitian Yang-Mills equations: Fαβ Fαβ 0, gαβFαβ 0, 1.1 where F is the associated field strength These equations cannot be solved analytically, the Donaldson-Uhlenbeck-Yau theorem 8, 9 states that, on a holomorphic poly stable bundle, there exists a unique connection that solves 1.1. Each of the heterotic vacua comes in two pieces: a Calabi-Yau threefold X and a holomorphic stable vector bundle V thereon. Monad vector bundles 11 will be constructed thereon, equivalent of turning on internal gauge fluxes over the Calabi-Yau threefolds.
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