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

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- Solution vii

Solution

For the magnetic theory,

b_{0}^{mag} = 3 (N_{c} + 1) - N_{f} = 2 N_{f} - 3 (N_{c} + 1) .

It ceases to be asymptotically free when

N_{f} \leq \frac{3}{2} (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.

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