The magnetic superpotential $W\sim qMq$ must have <R-charge> two, so
$$
R[M]=2-2R[q]=2\left(1-\frac{N_c+1}{N_f}\right).
$$
Therefore
$$
\boxed{\Delta(M)=\frac32R[M]
=3\left(1-\frac{N_c+1}{N_f}\right)},
$$
exactly matching the R-charge and dimension of the electric meson $\Phi^i\Phi^j$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 307 / 4 / vi / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-307/4/vi/solution