$\sum_i r_i=N_c$, corresponding to different ways of partitioning the $N_c$ eigenvalues among the $m$ critical points $c_i$ . In this case one finds in the infrared a decoupled set of theories with gauge groups $SU(r_l)$ and superpotentials of the form  with $k=n_l$ (see ). Therefore, the deformations  connect theories with different $k$ in  and unify them into a single framework.

It is often possible to deduce non-trivial properties of the theory  by studying the deformed theories . As a simple example , turning on small $s_i$ in  and using the fact that the resulting SQCD theories have stable vacua iff all $r_i\le N_f$ one deduces that the theory  has a vacuum iff We will see other examples below.

The main result of was that the strongly coupled infrared physics of theory  can be studied using a dual description in terms of a “magnetic” supersymmetric gauge theory with gauge group $\bar G=SU(\bar N_c)$, $\bar N_c=kN_f-N_c$, and the following matter content: $N_f$ flavors of (dual) quarks, $q_{\bar i}^{\bar\alpha}$, $\tilde q^{\bar j}_{\bar \beta}$, an adjoint superfield $Y_{\bar\alpha}^{\bar\beta}$, and gauge singlets $(M_j)_{\tilde i}^i$ representing the generalized mesons, of the original, “electric” theory. The mesons $M_j$ have in the magnetic theory standard kinetic terms $\int 