W-algebra conjecture for the VOAs of $(J^b[k],Y)$ Argyres-Douglas theories

Let $(J^b[k],Y)$ be an indecomposable Argyres-Douglas theory, where $J^b[k]$ denotes an irregular singularity and $Y$ is a regular singularity. Let $h$ be the dual Coxeter number of $J$, and set

$$k_{2d}=-h+\frac{b}{b+k}.$$

The nilpotent orbit, equivalently the $SU(2)$ embedding into $J$, associated with $Y$ specifies a quantum Drinfeld–Sokolov reduction of the affine Kac–Moody algebra $\widehat{J}_{k_{2d}}$. W-algebra conjecture. The VOA corresponding to $(J^b[k],Y)$ is

$${\cal W}^{k_{2d}}(J,Y),$$

where ${\cal W}^{k_{2d}}(J,Y)$ is this quantum Drinfeld–Sokolov reduction. This extends the proposed VOA descriptions for theories with irreducible irregular punctures and generalizes the class ${\cal S}$ construction; the source gives no resolution of the general claim.