relation: It is highly non-trivial, and will be shown in section [*4*]{}, that the scale matching relation  which is completely determined by global symmetries, is consistent with all possible deformations of the theory, such as turning on masses for the quarks $Q^i$, giving expectation values to the mesons $M_j$ , and deforming the theory to non-zero $s_i$ . The numerical constant $C$ in  is also fixed by the flows, $C=1$, and its value and in particular its independence of $N_f$, $N_c$, $k$ lead to additional tests of duality.

We view the consistency of  with deformations as strong evidence for the validity of the electric-magnetic duality hypothesis of .

When the electric superpotential is deformed to  the electric theory develops a large number of vacua labeled by ($r_1$, $\cdots$, $r_m$), with $\sum r_i=N_c$ (see the discussion after ). The $SU(r_l)$ theory contains an adjoint field with superpotential $W\simeq
X^{n_l+1}$. The magnetic theory has a similar structure obtained by analyzing vacua of the superpotential . Its vacua are labeled by integers ($\bar r_1, \cdots, \bar r_m$), $\sum \bar r_i=\bar N_c$. Classically, the moduli spaces do not agree. However when we include the quantum stability constraints  we find a one to one correspondence 