The Geometry of Generations
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 CalabiYau, Grassmannian, and toric signatures, which sensitively depend on the number of generations of leptons, as well as inclusion of Majorana mass terms for righthanded neutrinos. We speculate as to why three generations is special.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 October 2015
 DOI:
 10.1007/s0022001524167
 arXiv:
 arXiv:1408.6841
 Bibcode:
 2015CMaPh.339..149H
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Phenomenology;
 Mathematics  Algebraic Geometry
 EPrint:
 51 pages, 7 tables