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arXiv · 1408.6841

The Geometry of Generations

Yang-Hui He·Vishnu Jejjala·Cyril Matti·Brent D. Nelson·Michael Stillman
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Abstract

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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Yang-Hui He, Vishnu Jejjala, Cyril Matti, Brent D. Nelson, Michael Stillman. 2014-08-28. The Geometry of Generations. https://arxiv.org/abs/1408.6841

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