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

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- Solution iv

Solution

A free scalar has scaling dimension one. Setting the meson dimension to one gives

3 (1 - \frac{N _{c} + 1}{N _{f}}) = 1, N_{f} = \frac{3}{2} (N_{c} + 1) .

The expected interacting supersymmetric conformal window is therefore

\frac{3}{2} (N_{c} + 1) < N_{f} < 3 (N_{c} + 1) .

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