W algebras, cosets and VOAs for 4d N=2 SCFTs from M5 branes

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 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.