need to be lifted from the spectrum by a superpotential term, which is generically non-renormalizable except for the case $M=2$ (see below). Thus for the general $SU(M)^N$ case we do not completely succeed in generating the model from a renormalizable dynamics as in the non-supersymmetric case. For this choice of matter content an extra layer of perturbative or non-perturbative dynamics might be needed to get the non-renormalizable superpotentials as well. Once this superpotential (\[eq:supB\]) is added, the quantum modified constraint will ensure that the remaining $\Pi_{i=1}^{N} SU(M)_{2i-1}$ gauge groups are broken down to the diagonal $SU(M)$. In fact, as mentioned above, after confinement the meson matrix $\mathcal{M}_i$ will just play the role of the bifundamentals $Q_i$ of (\[fieldcontent\]) while ${\rm det} \mathcal{M}_i$ gives the invariants $B_i$, and so the full dynamically generated superpotential in the remaining $SU(M)^N$ theory is just, $$\label{eq:sup}
\frac{1}{\mu^{M-2}} \sum_i (L_i \mathcal{B}_i + \tilde{L}_i \tilde{\mathcal{B}}_i)
+
\frac{1}{\Lambda_2^{2M-2}} \sum_i S_i (B_i- \mathcal{B}_i \tilde{\mathcal{B}}_i -\Lambda^{2M}_2),$$ where $S_i$ are non-propagating Lagrange multiplier chiral superfields. Integrating out the fields $\mathcal{B}_i, \tilde{\mathcal{B}}_i$ and $L_i$ we are exactly left with the superpotential of (\[suppot\]), except that the symmetry breaking scale $v$ is now given by $\Lambda_2$, and because the fields $Q_i=\mathcal{M}_i$ themselves are 