Let $\mathcal {U} $ be a braided tensor category, typically unknown, complicated and in
particular non-semisimple. We characterize $\mathcal {U} $ under the assumption that there …

Let $ V $ be an $\mathbb {N} $-graded, simple, self-contragredient, $ C_2 $-cofinite vertex
operator algebra. We show that if the $ S $-transformation of the character of $ V $ is a linear …

Modular functors are traditionally defined as systems of projective representations of
mapping class groups of surfaces that are compatible with gluing. They can formally be …

We prove that the Kazhdan-Lusztig category of sl ˆ m at level k, KL k (sl m), is a semi-simple,
rigid braided tensor category for all even m≥ 4, and k=− m+ 1 2. Moreover, all modules in …

Various monoidal categories, including suitable representation categories of vertex operator
algebras, admit natural Grothendieck-Verdier duality structures. We recall that such a …

The classifying spaces of handlebody groups form a modular operad. Algebras over the
handlebody operad yield systems of representations of handlebody groups that are …

We prove a general mirror duality theorem for a subalgebra U of a simple conformal vertex
algebra A and its commutant V= Com A (U). Specifically, we assume that A≌⊕ i∈ IU i⊗ V i …

Let Oc be the category of finite-length modules for the Virasoro Lie algebra at central charge
c whose composition factors are irreducible quotients of reducible Verma modules. For any …

This book studies using string-net models to accomplish a direct, purely two-dimensional,
approach to correlators of two-dimensional rational conformal field theories. The authors …

It is a common and often repeated saying that for any quantum field theory the ultimate goal
is to solve the theory. Alas, already specifying in concrete terms the very meaning of this …