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

In the proposed Spin(8) theory, the gaugino contributes $I(\mathrm{adj})=6$ to the mixed gauge-R anomaly. The $p$ fields $q$ have superfield R-charge one, so their fermions contribute zero. The spinor $t$ has fermion R-charge $-5-1=-6$ and index one, giving $-6$. The singlets $M$ and $U$ do not enter the gauge anomaly. Henceand the proposed R-symmetry survives quantization.