are given by $B_i={\rm det}\,Q_i,\, i=1,\dots,N$; and $T_i={\rm tr}\,(Q_1\cdots Q_N)^i,\,i=1,\dots,M-1$. An expectation value of the operator $B_i$ will break $SU(M)_{i}\times SU(M)_{i+1}$ to an $SU(M)$ subgroup, leaving a theory with the same structure as the original theory, but with one fewer $SU(M)$ factor in the gauge group. Once all the $B_i$’s have expectation values the gauge group is broken to a single $SU(M)$. During this sequential breaking all the fields from the first $N-1$ $Q_i$’s will become massive due to the supersymmetric Higgs mechanism (some scalars will be eaten by the heavy gauge bosons), except the fields corresponding to the trace of $Q_i$, which are then described by the composite moduli field $B_i$. However, giving an expectation value to the last operator $B_N$ does not break the gauge group any further, and so one expects that the field $Q_N$ remains massless, and forms an adjoint and scalar of the unbroken $SU(M)$ gauge group. The invariants corresponding to the remaining adjoint are given by the operators $T_i$ above. Without further modification of the model, at a generic point in moduli space the theory will have $M-1$ unbroken $U(1)$ gauge groups and no charged fields under those $U(1)$’s. The behavior of the gauge 