A bstract Every four-dimensional\(\mathcal {N}= 2\) superconformal field theory comes
equipped with an intricate algebraic invariant, the associated vertex operator algebra. The …

The Schur limit of the superconformal index of a four-dimensional N= 2 superconformal field
theory encodes rich physical information about the protected spectrum of the theory. For a …

We prove the conjecture of Gaiotto and Rap\v {c}\'ak that the $ Y $-algebras $ Y_ {L, M,
N}[\psi] $ with one of the parameters $ L, M, N $ zero, are simple one-parameter quotients of …

4D N= 2 superconformal field theories and their invariants can be often enriched by nonlocal
Bogomol'nyi-Prasad-Sommerfield operators. In this paper we study the flavored Schur index …

A bstract We conjecture a formula for the Schur index of four-dimensional\(\mathcal {N}= 2\)
theories in the presence of boundary conditions and/or line defects, in terms of the low …

We introduce the notion of quasi-lisse vertex algebras, which generalizes admissible affine
vertex algebras. We show that the normalized character of an ordinary module over a quasi …

A bstract We investigate superconformal surface defects in four-dimensional\(\mathcal {N}=
2\) superconformal theories. Each such defect gives rise to a module of the associated chiral …

A bstract We present free field realizations for the associated vertex operator algebras of a
number of four-dimensional\(\mathcal {N}\)= 2 superconformal field theories. Our …

We give a functorial construction of the genus zero chiral algebras of class $\mathcal {S} $,
that is, the vertex algebras corresponding to the theory of class $\mathcal {S} $ associated …

These are lecture notes from author's mini-course on W-algebras during Session 1:“Vertex
algebras, W-algebras, and application” of INdAM Intensive research period “Perspectives in …