Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 307 / 4 / v / Solution

Gauge invariance, $SU(p)$ flavor symmetry and R-charge two permitwith the Spin(8) vector and spinor indices contracted by their invariant bilinear forms. Indeed, $R[Mqq]=0+1+1=2$ and $R[Utt]=12-5-5=2$. Powers of the matching scale can be inserted to give fields whichever canonical mass dimensions are chosen.