superfield $s_0$ is then seen to transform under the $U(1)_R$ symmetries  with charge $B_0=2-(k+1)B_a$. Therefore, only the $U(1)_R$ symmetry under which the charge of the adjoint field $X$ is $B_a=2/(k+1)$ leaves the vacuum with $\langle s_0\rangle= s_0$ invariant, and corresponds to a good symmetry. The unbroken global symmetry of the model is: The matter fields $Q$, $\tilde Q$ and $X$ transform under this global symmetry as follows:

We will also be interested in more general superpotentials: $\lambda$ is a Lagrange multiplier enforcing the condition ${\rm Tr}
X=0$. The coupling constant $s_i$ has dimension $2-k+i$ and $U(1)_R$ charge $B_i=2-(k+1-i)B_a$. For non zero $\{s_i\}$  breaks both $R$ symmetries . The space of theories labeled by the $\{s_i\}$ describes rather rich dynamics. Using transformations in $SU(N_c)_{\IC}$ one can diagonalize the matrix $X$. For generic $\{s_i\}$, such that with all eigenvalues $c_i$ different from each other, the theory splits in the infrared into a set of decoupled SQCD theories. Ground states are labeled by sequences of integers $r_1\le
r_2\le\cdots\le r_k$, where $r_l$ is the number of eigenvalues of the matrix $X$ residing in the $l$’th minimum of the potential $V=|W^\prime(x)|^2$. Clearly, $\sum_{l=1}^kr_l=N_c$. $\lambda$ in  is determined by requiring that the sum of the eigenvalues 