of the quantum vacua in the two theories. The vacuum map is non trivial:

A class of operators that was discussed in , and will be revisited in section [*5*]{}, are the baryon-like operators: where $\sum_i n_i=N_c$. The duality map relating the baryons $B$ , and the analogously defined dual baryons $\bar B$ is: where $\bar n_l=N_f-n_{k+1-l}$, $l=1,\cdots, k$, and $P$ is a phase that will be discussed in section [*5*]{}. The form of  is determined by global symmetries, while the overall numerical constant is uniquely fixed by the flows, and it is non-trivial that it is consistent with the deformations, such as . This compatibility will be established in section [*5*]{}.

In addition to the mesons  and baryons , the chiral ring of the electric (magnetic) theory contains the generators ${\rm Tr} X^j$ (${\rm Tr} Y^j$), $j=2,\cdots, k$. Global symmetries require (up to terms depending on the quarks which we will determine below) that with $f_j$ calculable numerical constants. In the next section we will calculate $f_j$ and describe the generalization of  to the deformed theories .

The duality map described in this section may be used to study the physics of the theory  at strong coupling using a 