Gauge invariance, $SU(p)$ flavor symmetry and R-charge two permit
$$
\boxed{W=M^{ij}q_iq_j+Utt},
$$
with 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.


Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-307/4/v/solution