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The Geometry of Generations

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.

preprint2014arXivOpen access
Yang-Hui HeVishnu JejjalaCyril MattiBrent D. NelsonMichael Stillman
hep-phmath.AGhep-th
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Yang-Hui HeVishnu JejjalaCyril MattiBrent D. NelsonMichael Stillman

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