Calabi-Yau manifolds in weighted \({\mathbb{P}}_4\). (English) Zbl 0962.14029

Summary: It has recently been recognized that the relation between exactly solvable conformal field theory compactifications of the heterotic string and Calabi-Yau manifolds necessarily involves the discussion of embeddings in weighted projective space. We therefore study this class of manifolds more closely. We have constructed a subclass of these spaces and find that this class features a surprising symmetry under \(\chi\to-\chi\). Furthermore, we show that this class is potentially of much greater interest with regard to phenomenologically viable models, as there are 25 three-generation models among these manifolds.


14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
32Q25 Calabi-Yau theory (complex-analytic aspects)
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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