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 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 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 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 …

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) …

We study logarithmic conformal field models that extend the (p, q) Virasoro minimal models.
For coprime positive integers p and q, the model is defined as the kernel of the two minimal …

We provide a ribbon tensor equivalence between the representation category of small
quantum SL. 2/, at parameter q D ei= p, and the representation category of the triplet vertex …

We give a new factorizable ribbon quasi-Hopf algebra U, whose underlying algebra is that of
the restricted quantum group for s ℓ (2) at a 2 p th root of unity. The representation category …