Genus-zero class S chiral algebras

Let a class $\mathcal{S}$ SCFT of type $A_n$ be obtained from the six-dimensional $(2,0)$ theory on a UV curve of genus zero. Let $W_i$ denote singlet generators of the protected chiral algebra, and let the additional currents correspond to generators of the four-dimensional Higgs-branch chiral ring.

Genus-zero chiral algebra conjecture. The protected chiral algebra is a $\mathcal{W}$-algebra with singlet generators $W_i$, $i=1,\ldots,n$, of dimension $i+1$, together with additional currents associated to Higgs-branch chiral-ring generators of the four-dimensional theory. In special cases some $W_i$ may be composites; in particular, when the central charge equals its Sugawara value with respect to the affine currents, the stress tensor $W_1(z)$ is composite.

This extrapolates the proposed description of the $T_n$ chiral algebras to all genus-zero class $\mathcal{S}$ theories. The source describes it as not extremely well-supported, so its general validity remains open.