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 …

Let V be a simple vertex operator algebra containing a rank n Heisenberg vertex algebra H
and let C= Com (H; V) be the coset of H in V. Assuming that the module categories of interest …

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 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 …

Let V be a simple vertex operator algebra (VOA) and consider a representation category of V
that is a vertex tensor category in the sense of Huang–Lepowsky. In particular, this category …

The two pillars of rational conformal field theory and rational vertex operator algebras are
modularity of characters, and the interpretation of its category of modules as a modular …

We prove the longstanding physics conjecture that there exists a unique two-parameter
${\mathcal {W}} _ {\infty} $-algebra which is freely generated of type ${\mathcal {W}}(2 …

The main result is that the category of ordinary modules of an affine vertex operator algebra
of a simply laced Lie algebra at admissible level is rigid and thus a braided fusion category …