The Geometry of Generations

He, Y., Jejjala, V., Matti, C., Nelson, B. D. & Stillman, M. (2015). The Geometry of Generations. Communications in Mathematical Physics, 339(1), pp. 149-190. doi: 10.1007/s00220-015-2416-7

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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.

Item Type: Article
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-015-2416-7
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Engineering
URI: http://openaccess.city.ac.uk/id/eprint/12861

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