The Geometry of Generations

2014/08/28 by He, Yang-Hui, Jejjala, Vishnu, Matti, Cyril +2 · 4 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.1408.6841

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.

Cited by

• Classification of minimal models producing b, c and tau masses at one-loop level
• Vacuum Geometry of the Standard Model
• The Vacuum Moduli Space of the Minimal Supersymmetric Standard Model
• Topological Freeze-out by Semi-Annihilation

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