$Sp(4)$ subgroup. In our case, below the scale $\Lambda_2$ where the first set of $SU(2)$’s confines the global symmetry is raised to a gauge symmetry in which case the effect of confinement is to break the gauged $SU(2)\times SU(2)\subset
SU(4)$ to a single $SU(2)$. In the process three scalars are eaten and three remain (of the six “mesons” $\mathcal{M}'_{ij}$). Of the three massless scalars that remain, two are given a mass by the tree level superpotential (\[eq:supB\]) as described above, and the Pfaffian becomes massive by the quantum modified constraint. The tree level superpotential and the fact that only a subgroup of the global symmetries is gauged explicitly breaks the $SU(4)$ “global” symmetry down to $SU(2)\times SU(2)$. Alternatively, the constraint can be incorporated in the theory as before by adding a superpotential, $$S({\rm Pf}\,\mathcal{M}'-\Lambda_2^4),$$ where $S$ is the Lagrange multiplier which enforces the constraint. Fluctuations of the Pfaffian then obtain a mass by the Lagrange multiplier. Hence, we have demonstrated that the supersymmetric version of the $SU(2)^N$ theory which is dual to the higher dimensional latticized $SU(2)$ theory can be generated dynamically, while for larger gauge groups one has to add a non-renormalizable superpotential if one assumes the minimal matter 