For the magnetic theory,
$$
b_0^{\rm mag}=3(\widetilde N_c+1)-N_f
=2N_f-3(N_c+1).
$$
It ceases to be asymptotically free when
$$
\boxed{N_f\le\frac32(N_c+1)}.
$$
This is precisely the lower edge of the electric conformal window. Inside the window both descriptions flow to the same interacting <infrared fixed point>; below it the magnetic variables provide a weakly coupled infrared description.

Solution

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

 Solution

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