Interacting Topological Superconductors and possible Origin of $16n$ Chiral Fermions in the Standard Model
Abstract
Motivated by the observation that the Standard Model of particle physics (plus a righthanded neutrino) has precisely 16 Weyl fermions per generation, we search for $(3+1)$dimensional chiral fermionic theories and chiral gauge theories that can be regularized on a 3 dimensional spatial lattice when and only when the number of flavors is an integral multiple of 16. All these results are based on the observation that local interactions reduce the classification of certain $(4+1)$dimensional topological superconductors from $\mathbb{Z}$ to $\mathbb{Z}_{8}$, which means that one of their $(3+1)$dimensional boundaries can be gapped out by interactions without breaking any symmetry when and only when the number of boundary chiral fermions is an integral multiple of $16$.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.4151
 Bibcode:
 2014arXiv1402.4151Y
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 5 pages, 2 figures