of the various terms in  can be calculated using flows, and will be derived below. The function $\alpha_s(t)$ will be computed too.

The magnetic superpotential  can be used to find the operator map relating the operators $\Tr Y_s^j$ to the electric ones. Differentiating the generating functional with respect to the couplings $t_{k+1-j}$ one can derive the map of the operators The function $\alpha_s$ in  is important because it contributes to the map of the operators .

Note that  describes the duality map in the coordinates on theory space described above, $\{t_i\}$. $Y_s$ is the adjoint field in those coordinates (see section [*3*]{}). The relatively simple form of the map is in fact the main motivation behind the coordinate transformation $s\to t$. In the original $s$ variables the duality map is significantly more complicated. Its precise form will be exhibited below.

The discussion of the classical and quantum moduli space and chiral ring for the theory  is essentially identical to the electric case, replacing $N_c, r_l\to \bar N_c, \bar r_l$. The classical electric and magnetic moduli spaces are different; they have different numbers of disconnected components (labeled by $\{r_i\}$, $\{\bar r_i\}$ respectively). Similarly, the classical chiral rings are different. Since the 