W algebras, cosets and VOAs for 4d N $$ \mathcal{N} $$ = 2 SCFTs from M5 branes

A bstract 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 algebras defined using nilpotent orbit with partition [ q m , 1 s ]. Gauging above AD matters, we can find VOAs for more general $$ \mathcal{N} $$ 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.

Abstract licence: CC BY

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