content. This non-renormalizable superpotential should then be generated by some other physics at higher energies, either through non-perturbative effects or from integrating out heavy particles.

We begin with an $SU(M)^{2N}$ gauge theory with the periodic structure of (\[fieldcontent\]). We further assume that the gauge coupling of every even group in the chain of $SU(N)$’s is much larger than the neighboring odd ones: $g_2=g_{2i}\gg g_{2i-1}=g_1$, [*i.e.*]{}, $\Lambda_2= \Lambda_{2i} \gg \Lambda_{2i-1}= \Lambda_1$. Therefore, concerning the dynamics of any $SU(M)_{2i}$, the weaker gauge groups can be regarded as a weakly gauged global symmetry, leaving an $SU(M)_{2i}$ gauge theory with $M$ flavors in this sector of the theory. With this particular matter content it was shown in [@Seiberg] that the theory confines in the IR with chiral symmetry breaking, with the confined degrees of freedom given by $\mathcal{M}_i, \mathcal{B}_i,\tilde{\mathcal{B}}_i$ ($i=1\ldots N$), $$\begin{array}{c|c|ccrc}
& SU(M)_{2i}& SU(M)_{2i-1}& SU(M)_{2i+1}& U(1)_B & U(1)_R \\
\hline
\tilde{\mathcal{Q}}_i & \overline{{\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}}  & {\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}& 1 & 1 & 0 \\
\mathcal{Q}_i & {\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}& 1 & \overline{{\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}} & -1&  0\\
\hline
\hline
\tv{15}
\mathcal{M}_i= \mathcal{Q}_i \tilde{\mathcal{Q}}_i & &{\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}& \overline{{\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}} & 0 & 0\\
\mathcal{B}_i= \mathcal{Q}_i^M & & 1 & 1 & M & 0 \\
\tilde{\mathcal{B}}_i=\tilde{\mathcal{Q}}^M_i & & 1 & 1 & -M 