A free scalar has <scaling dimension> one. Setting the meson dimension to one gives
$$
3\left(1-\frac{N_c+1}{N_f}\right)=1,
\qquad
N_f=\frac32(N_c+1).
$$
The expected interacting <supersymmetric conformal window> is therefore
$$
\boxed{\frac32(N_c+1)<N_f<3(N_c+1)}.
$$

Solution

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

 Solution

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