extra dimensions
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In Refs. [@ACG; @Fermi1; @Fermi2], it has been argued that the low energy behavior of a purely 4D theory can be effectively described by the low-lying KK modes of a 5D theory compactified on a circle or an $S^1/Z_2$ orbifold. Here we will first present the supersymmetric versions of these theories, so that later we can use these to construct the 4D analogs of a higher dimensional mechanism for mediating supersymmetry breaking.

The theory we will consider is an asymptotically free four dimensional ${\cal N}$=1 supersymmetric $SU(M)^N$ gauge theory with chiral multiplets $Q_i$ in bifundamental representations as follows[^3]: $$\label{fieldcontent}
 \begin{array}{c|ccccc}
      & SU(M)_1 & SU(M)_2 & SU(M)_3 & \cdots & SU(M)_N \\ \hline
  Q_1 & {\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}& \overline{{\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}}  & 1       & \cdots & 1 \\
  Q_2 & 1       & {\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}& \overline{{\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}}  & \cdots & 1 \\
  \vdots & \vdots & \vdots & \vdots & \ddots & \vdots \\
  Q_N & \overline{{\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}} & 1 & 1 & \cdots & {\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}\end{array} \nonumber$$ The low-energy behavior of this theory was analyzed in Ref. [@CEFS]. Here we briefly summarize the relevant results from that analysis. The flat directions (moduli space) of the theory are described by the independent gauge invariant operators [@BDFS], which 