Just two pages on conformal manifolds and two rings of superconformal primary operators, following the first section of a recent paper by Gerchkovitz, Gomis, Ishtiaque, Karasik, Komargodski and Pufu.

The main point is that for a four-dimensional $\mathcal{N}=2$ theory, one usually defines the chiral ring, which has nice properties, like being freely generated. In fact, this ring should really be seen as associated to the Coulomb branch of the theory, as the number of generators is the dimension of the Coulomb branch. But this formulation then suggests the existence of a ring associated to the Higgs branch, which I perceive to be somewhat less known. This ring can be defined analogously, but is more complex in the sense that it is not freely generated.

Note that if we embed the four-dimensional SCA into the six-dimensional one, the "Higgs ring" corresponds to the special class of short $\frac{1}{2}$-BPS operators denoted by $\mathcal{D}[0,0,0;d_1 ,0]$, which form the $\frac{1}{2}$-BPS ring in six dimensions (see for instance a recent paper).