are stable. If, for example, we pick a classical vacuum  with one or more of the $r_l>N_f$, the resulting SQCD theory is destabilized by quantum effects . Hence, such classical vacua are not present in the quantum moduli space. Similarly, some of the vacua in the multicritical case are destabilized and are removed from the quantum moduli space.

The classical chiral ring can be thought of as the ring generated by the operators $\Tr X^j$ subject to two classes of constraints. The first comes from the equation of motion which follows from the superpotential , $W^\prime=0$. The second comes from the characteristic polynomial of $X$, and is an example of a relation following from the composite nature of gauge invariant operators mentioned above.

Quantum mechanically one expects on general grounds to find new relations in the chiral ring corresponding to the quantum reduction of the moduli space described above. It is in principle possible to construct these relations by requiring that imposing them has the effect of removing exactly the vacua that we know from our previous discussion should be removed, but this is very difficult in practice as well as unmotivated. Duality provides an elegant general solution to the 