Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 305 / 4 / a / ii / Solution

For $b>0$, the theory is asymptotically free: it is weakly coupled at high energies and strongly coupled in the infrared. For $b<0$, the coupling decreases toward the infrared but grows toward a finite ultraviolet Landau pole; such a theory is infrared free and requires an ultraviolet completion before that pole.