weak coupling description in terms of magnetic variables. For example, one finds that this theory may exhibit at strong coupling a “free magnetic phase,” with the magnetic variables governed by a non-asymptotically free gauge theory. Some additional features are described in .

The classical chiral ring of the electric theory is generated by the generalized mesons $M_j$ , baryons  and traces of the adjoint matrix, $\Tr X^j$. The latter, which we will focus on here satisfy classically two sets of constraints, following from the equation of motion $W^\prime=0$,  and from the characteristic polynomial. Defining $f(p)\equiv\det(p-X)$, the constraint is $f(X)=0$. The two together give rise to a set of algebraic equations for the generators of the classical chiral ring. The solutions of these equations describe the ring of functions on the classical moduli space.

One can repeat the same construction for the magnetic theory. The discussion proceeds in complete parallel to that of the moduli space. Classically the chiral rings of the electric and magnetic theories cannot be the same: while the equation of motion $W^\prime=0$ gives similar relations for the generators, the characteristic polynomials give different sets of constraints, since the sizes of the matrices $X$ and $Y$ are different. 