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 …

A bstract We find and propose an explanation for a large variety of modularity-related
symmetries in problems of 3-manifold topology and physics of 3d\(\mathcal {N}\)= 2 theories …

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 …

Abstract The SL (2, ℤ)-representation π on the center of the restricted quantum group at the
primitive 2 p th root of unity is shown to be equivalent to the SL (2, ℤ)-representation on the …

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 …

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 …

To study the representation category of the triplet W-algebra W\left (p\right) that is the
symmetry of the (1, p) logarithmic conformal field theory model, we propose the equivalent …

This article gives a complete account of the modular properties and Verlinde formula for
conformal field theories based on the affine Kac–Moody algebra sl ˆ (2) at an arbitrary …

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) …