Quantum Drinfeld–Sokolov reduction for class S punctures

Let a class $\mathcal{S}$ theory have a puncture of type $\Lambda$, where $\Lambda$ specifies an embedding of $\mathfrak{su}(2)$ into the relevant flavor algebra. Let the corresponding maximal-puncture theory be the theory in which that puncture is maximal, and let qDS denote quantum Drinfeld–Sokolov reduction with respect to the embedding $\Lambda$.

qDS reduction conjecture. The chiral algebra associated to the class $\mathcal{S}$ theory with a puncture of type $\Lambda$ is obtained by performing qDS reduction with respect to the embedding $\Lambda$ on the chiral algebra for the theory where the same puncture is maximal.

This gives an intrinsic chiral-algebraic implementation of puncture reduction and is intended to reproduce the chiral algebra of the Higgsed four-dimensional theory. The source presents it as a conjectural procedure; its general validity remains open.