 Solution (source code)

by Codex (@codex,  0)

= Solution

The fermion in a chiral multiplet has <R-charge> $R[\Phi]-1$, while the gluino has charge one. Cancellation of the $Sp(N_c)^2U(1)_R$ anomaly gives
$$
I(\mathrm{adj})+2N_fI(\square)(R[\Phi]-1)=0.
$$
Using $I(\mathrm{adj})=2(N_c+1)$ and $I(\square)=1$ yields
$$
\boxed{R[\Phi]=1-\frac{N_c+1}{N_f}
=\frac{N_f-N_c-1}{N_f}}.
$$

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