On bosonic vertex algebras associated with 3D reductions of Argyres-Douglas theories

TL;DR

This paper explores bosonic vertex operator algebras linked to 3D reductions of Argyres-Douglas theories, proposing a complete set of generators and revealing embedded $W_3$ structures at specific central charges.

Contribution

It introduces a conjecture for the full set of strong generators of these VOAs, expanding understanding of their structure and subalgebra content.

Findings

Proposed a complete set of strong generators for the VOAs.

Identified $W_3$ subalgebras at $c=-2$ within the VOAs.

Connected 3D gauge theories with vertex algebra structures.

Abstract

We study the bosonic VOA associated with the 3D $\mathcal{N}=4$ abelian linear quiver gauge theories arising from compactifying 4D $\mathcal{N}=2$ Argyres-Douglas theories of $(A_1,A_{2n-1})$ and $(A_1,D_{2n})$ types. These VOAs are obtained by cancelling the gauge anomaly of the H-twisted 3D theory on the half-space by Heisenberg algebras on the boundary. We particularly conjecture a complete set of strong generators of these bosonic VOAs, which contains more than the Virasoro stress tensor and those arising from Higgs branch operators. We also find that these bosonic VOAs contain copies of the $W_3$ vertex algebra at $c=-2$ as sub vertex algebras.