Imperfect Mirrors of the Standard Model
  Inspired by the Standard Model of particle physics, we discuss a mechanism for constructing chiral, anomaly-free gauge theories. The gauge symmetries and particle content of such theories are identified using subgroups and complex representations of simple anomaly-free Lie groups, such as $SO(10)$ or $E_6$. We explore, using mostly $SO(10)$ and the $\mathbf{16}$ representation, several of these "imperfect copies" of the Standard Model, including $U(1)^N$ theories, $SU(5)\otimes U(1)$ theories, $SU(4)\otimes U(1)^2$ theories with 4-plets and 6-plets, and chiral $SU(3)\otimes SU(2)\otimes U(1)$. A few general properties of such theories are discussed, as well as how they might shed light on nonzero neutrino masses, the dark matter puzzle, and other phenomenologically relevant questions. 
Jeffrey M. Berryman, Andr\'e de Gouv\^ea, Daniel Hern\'andez, and   Kevin J. Kelly
hep-ph