W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branes

TL;DR

This paper identifies specific vertex operator algebras (VOAs) associated with 4d N=2 SCFTs from M5 branes, revealing new algebraic structures and dualities through their relation to 6d theories.

Contribution

It constructs VOAs for a class of Argyres-Douglas theories using W algebras and cosets, connecting 4d SCFTs with 2d VOA properties and dualities.

Findings

VOAs for AD matters are W algebras with nilpotent orbit partitions.

VOAs for general (A_{N-1}, A_{k-1}) theories are realized as cosets.

New properties like level-rank duality and conformal embeddings are derived.

Abstract

We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the $W$ algebra defined using nilpotent orbit with partition $[q^m,1^s]$. Gauging above AD matters, we can find VOAs for more general $\mathcal{N}=2$ SCFTs engineered from 6d $(2,0)$ theories. For example, the VOA for general $(A_{N-1}, A_{k-1})$ theory is found as the coset of a collection of above $W$ algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.