Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 305 / 3 / vi / Solution

For $N_f=3$, $q=3/2$. Under $SU(3{)}_L\times SU(3{)}_R\times U(1{)}_X$, the proposed left-handed composites transform asFor example, the charge of $\chi ={\bar{\psi }}_R{\lambda }_L{\psi }_L$ is $-1+3/2-1=-1/2$, and the antisymmetric product of two $SU(3)$ fundamentals is an antifundamental.