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This paper surveys the long-standing connections and impact between Vaughan Jones's
theory of subfactors and various topics in mathematical physics, namely statistical …

Moonshine forms a way of explaining the mysterious connection between the monster finite
group and modular functions from classical number theory. The theory has evolved to …

We completely classify diffeomorphism covariant local nets of von Neumann algebras on the
circle with central charge c less than 1. The irreducible ones are in bijective correspondence …

Let V be a simple vertex operator algebra and G a finite automorphism group of V such that
VG is regular. It is proved that every irreducible V G-module occurs in an irreducible g …

The quantum dimensions of modules for vertex operator algebras are defined and their
properties are discussed. The possible values of the quantum dimensions are obtained for …

By a pointed vertex operator algebra (VOA) we mean one whose modules are all simple
currents (ie invertible), eg lattice VOAs. This paper systematically explores the interplay …

A bstract In a physical system undergoing a continuous quantum phase transition,
spontaneous symmetry breaking occurs when certain symmetries of the Hamiltonian fail to …

We prove the first nontrivial reconstruction theorem for modular tensor categories: the
category associated to any twisted Drinfeld double of any finite group, can be realised as the …

The aim of the paper is twofold. First, we show that a quantum field theory A living on the line
and having a group G of inner symmetries gives rise to a category G–Loc A of twisted …