On the 4d/3d/2d view of the SCFT/VOA correspondence

Abstract

We start with the SCFT/VOA correspondence formulated in the Omega-background approach, and connect it to the boundary VOA in 3d $\mathcal{N}=4$ theories and chiral algebras of 2d $\mathcal{N}=(0,2)$ theories. This is done using the dimensional reduction of the 4d theory on the topologically twisted and Omega-deformed cigar, performed in two steps. This paves the way for many more interesting questions, and we offer quite a few. We also use this approach to explain some older observations on the TQFTs produced from the generalized Argyres-Douglas (AD) theories reduced on the circle with a discrete twist. In particular, we argue that many AD theories with trivial Higgs branch, upon reduction on $S^1$ with the $\mathbb{Z}_N$ twist (where $\mathbb{Z}_N$ is a global symmetry of the given AD theory), result in the rank-0 3d $\mathcal{N}=4$ SCFTs, which have been a subject of recent studies. A generic AD theory, by the same logic, leads to a 3d $\mathcal{N}=4$ SCFT with zero-dimensional Coulomb branch (and suggests that there are a lot of them). Our construction therefore puts various empirical observations on the firm ground, such as, among other things, the match between the 4d VOA and the boundary VOA for some 3d rank-0 SCFTs previously observed in the literature. We end with an extensive list of promising open problems.