Number of fermion generations from a novel grand unified model by Pritibhajan Byakti and others (2014, 10.1140/epjc/s10052-014-2730-9)

Authors: Pritibhajan Byakti, David Emmanuel-Costa, Arindam Mazumdar and Palash B. Pal.

Official publication: link.springer.com/article/10.1140/epjc/s10052-014-2730-9

Section 3 gives the Standard Model branching rules of the $SU(6)$ representations $\overline{6}$ and $15$. Their cubic gauge anomaly coefficients are $-1$ and $2$, respectively; one $15$ with two $\overline{6}$ therefore cancels this gauge anomaly. Additional charged fermions can form a vectorlike gauge spectrum with invariant mass terms.