We exploit the recently developed software package LieART to show that $\mathrm{SU}(N)$ grand unified theories with chiral fermions in mixed tensor irreducible representations can lead to standard model chiral fermions without additional light exotic chiral fermions; i.e., only standard model fermions are light in these models. Results are tabulated which may be of use to model builders in the future. An SU(6) toy model is given and model searches are discussed.

• Received 5 June 2015

DOI:https://doi.org/10.1103/PhysRevD.92.035005