can be modified \[\]. We will see that it may also happen that new relations in the chiral ring appear quantum mechanically. Then, the classical chiral ring is truncated, in some cases rather dramatically.

The purpose of this paper is to study some qualitative and quantitative features of the duality of  in a class of examples that exhibit the phenomena mentioned above and a rich duality structure which helps in analyzing them. In the rest of this section we will describe the models we will study and state the main results. Derivations and many additional details appear in subsequent sections.

*The electric theory*

Consider a $G=SU(N_c)$ gauge theory with an adjoint field $X$ and $N_f$ quarks $Q^i$ and $\tilde Q_{\tilde i}$ ($i,\tilde i=1,...,N_f$) in the fundamental and anti-fundamental representations of the gauge group, respectively. These theories are still not fully understood (see however a discussion below in section [*7*]{}). When a superpotential is turned on, the dynamics simplifies. At first sight the fact that the high order polynomials appearing in  can have any effect on the physics is surprising. Indeed, the presence of these non-renormalizable interactions seems irrelevant for the long distance behavior of the theory, which will be our 