The Geometry of Generations
High Energy Physics - Theory
2014-09-01 v1 High Energy Physics - Phenomenology
Algebraic Geometry
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.
Cite
@article{arxiv.1408.6841,
title = {The Geometry of Generations},
author = {Yang-Hui He and Vishnu Jejjala and Cyril Matti and Brent D. Nelson and Michael Stillman},
journal= {arXiv preprint arXiv:1408.6841},
year = {2014}
}
Comments
51 pages, 7 tables