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

TL;DR

This paper explores the connections between 4d, 3d, and 2d supersymmetric theories through the SCFT/VOA correspondence, using dimensional reduction and Omega-background techniques to relate various boundary and chiral algebras, and clarifies some previous empirical observations.

Contribution

It introduces a new dimensional reduction approach connecting 4d SCFTs, boundary VOAs, and 2d chiral algebras, providing a theoretical foundation for earlier empirical findings.

Findings

Many Argyres-Douglas theories reduce to rank-0 3d SCFTs with trivial Higgs branches.

The approach explains the match between 4d VOAs and boundary VOAs in certain 3d SCFTs.

The paper proposes new open problems in the field.

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.