$s_i$ can also be fine tuned to yield multicritical infrared behavior, whose consistency with duality puts further constraints on the structure described in sections [*2, 3*]{}.

In section [*5*]{} we study the baryon operators in the theory and show that they are mapped correctly between the electric and magnetic theories. This provides additional non-trivial checks of duality and the explicit coefficients in the magnetic superpotential.

In section [*6*]{} we illustrate the general results with a few examples. In particular, we show that in some cases the quantum relations in the chiral ring lead to qualitative changes in the structure of the chiral ring. We conclude with some comments about the theory with no superpotential in section [*7*]{}. Two appendices contain a discussion of dangerously irrelevant operators and some useful identities about polynomial equations which are used in the text.

We start with a review of the results of on supersymmetric Yang-Mills theory with gauge group $G=SU(N_c)$ coupled to a single chiral matter superfield $X_\alpha^\beta$ in the adjoint representation of the gauge group, and $N_f$ flavors of fundamental representation superfields, $Q^i_\alpha$, $\tilde Q_j^\beta$; $\alpha,
\beta=1,\cdots, N_c$; $i,j=1,\cdots, N_f$. This theory is in a non-Abelian Coulomb phase for all $N_f\ge1$. Its anomaly 