We review the construction of braided tensor categories and modular tensor categories from
representations of vertex operator algebras, which correspond to chiral algebras in physics …

We show that if $ T $ is a simple non-negatively graded regular vertex operator algebra with
a nonsingular invariant bilinear form and $\sigma $ is a finite order automorphism of $ T …

Logarithmic conformal field theories (LCFT) play a key role, for instance, in the description of
critical geometrical problems (percolation, self-avoiding walks, etc), or of critical points in …

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 …

Trialities of W-algebras are isomorphisms between the affine cosets of three different W-
(super) algebras, and were first conjectured in the physics literature by Gaiotto and Rapčák …

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 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 relate commutative algebras in braided tensor categories to braid-reversed tensor
equivalences, motivated by vertex algebra representation theory. First, for C a braided …

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 …

A bstract We formulate a conjectural relation between the category of line defects in
topologically twisted 3d\(\mathcal {N}\)= 4 supersymmetric quantum field theories and …