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The Geometry of Generations

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arxiv 1408.6841 v1 pith:S6NNINXQ submitted 2014-08-28 hep-th hep-phmath.AG

Yang-Hui He , Vishnu Jejjala , Cyril Matti , Brent D. Nelson , Michael Stillman This is my paper · ORCID
classification hep-thhep-phmath.AG
keywords generationsalgebraicgeometryspacecalabi-yaucomputedependdoublets
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We present an intriguing and precise interplay between algebraic geometry and the phenomenology of generations of particles. Using the electroweak sector of the MSSM as a testing ground, we compute the moduli space of vacua as an algebraic variety for multiple generations of Standard Model matter and Higgs doublets. The space is shown to have Calabi-Yau, Grassmannian, and toric signatures which sensitively depend on the number of generations of leptons, as well as inclusion of Majorana mass terms for right-handed neutrinos. We speculate as to why three generations is special.

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  1. Vacuum Geometry of the Standard Model

    hep-th 2025-06 conditional novelty 7.0 of 10

    The vacuum moduli space of the MSSM is shown to consist of three rational components of dimensions 1, 15, and 29 via Gröbner basis computations.

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