problem, explaining why such new relations appear in the quantum chiral ring and providing a constructive way of determining them.

*The magnetic theory.*

It was shown in that in the presence of a superpotential  there exists a simple dual magnetic description. It is similar to the original electric theory but based on the gauge group $SU(\bar N_c=kN_f-N_c)$ with an adjoint field $Y$ and $N_f$ quarks $q_i$ and $\tilde q^{\tilde i}$ in the fundamental and anti-fundamental representations as well as some gauge invariant fields $(M_j)^i_{\tilde i}$ which correspond to the composite operators where the suppressed color indices are summed over (when $s_1 \not= 0$ we find it convenient to define $M_j$ in terms of $X_s$). The magnetic theory has a superpotential where the shifted field $Y_s$ is defined similarly to $X_s$ so that the coefficient of $\Tr Y_s^k$ in the magnetic superpotential vanishes. The auxiliary scale $\mu$ is needed for dimensional reasons; note that even though the fields $M_j$ are elementary in the magnetic description, the identification  implies that they are assigned scaling dimension $j+1$. Therefore, $\mu$ in  has indeed dimensions of mass. One could redefine $M_j$ by powers of $\mu, s_0$ to make their kinetic terms canonical. The numerical coefficients 