Starting with a gentle approach to the Alday–Gaiotto–Tachikawa (AGT) correspondence
from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on …

We construct a family of 3d quantum field theories $\mathcal T_ {n, k}^ A $ that conjecturally
provide a physical realization--and derived generalization--of non-semisimple mathematical …

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 …

Let $ V $ be a vertex operator algebra with a category $\mathcal {C} $ of (generalized)
modules that has vertex tensor category structure, and thus braided tensor category …

We define new deformable families of vertex operator algebras A g, Ψ, σ A g, Ψ, σ
associated to a large set of S-duality operations in four-dimensional supersymmetric gauge …

We construct two non-semisimple braided ribbon tensor categories of modules for each
singlet vertex operator algebra M (p), p≥ 2. The first category consists of all finite-length M …

We show that the category of finite-length generalized modules for the singlet vertex algebra
M (p), p∈ Z> 1, is equal to the category OM (p) of C 1-cofinite M (p)-modules, and that this …

We establish rigid tensor category structure on finitely-generated weight modules for the
subregular W-algebras of sl n at levels-n+ nn+ 1 (the B n+ 1-algebras of Creutzig–Ridout …

Abstract We prove Feigin-Frenkel type dualities between subregular W-algebras of type A, B
and principal W-superalgebras of type sl (1| n), osp (2| 2 n). The type A case proves a …

We show that there is a braided tensor category structure on the category of C 1-cofinite
modules for the (universal or simple) Virasoro vertex operator algebras of arbitrary central …