This article aims to review a selection of central topics and examples in logarithmic
conformal field theory. It begins with the remarkable observation of Cardy that the horizontal …

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 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 …

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 study the triplet vertex operator algebra W (p) of central charge 1− 6 (p− 1) 2p, p⩾ 2. We
show that W (p) is C2-cofinite but irrational since it admits indecomposable and logarithmic …

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 …

This is the first part in a series of papers in which we introduce and develop a natural,
general tensor category theory for suitable module categories for a vertex (operator) …

By studying the properties of q-series Z^-invariants, we develop a dictionary between 3-
manifolds and vertex algebras. In particular, we generalize previously known entries in this …

A bstract Logarithmic conformal field theories have a vast range of applications, from critical
percolation to systems with quenched disorder. In this paper we thoroughly examine the …

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 …