Conformal Field Theories and Tensor Categories

The present volume is a collection of seven papers that are either
based on the talks presented at the workshop "Conformal field theories and tensor categories" held June 13 to June 17, 2011 at the
Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond
rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researcherslooking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications

From Hopf algebras to tensor categories.- Pattern-of-zeros approach to Fractional quantum Hall states and a classification of symmetric polynomial of infinite variables.- Virasoro central changes for Nichols algebras.- Logarithmic bulk and boundary conformal field theory and the full centre construction.- Logarithmic tensor category theory for generalized modules for a conformal vertex algebra, I: Introduction and strongly graded algebras and their generalized modules.- C2-cofinite w-algebras and their logarithmic representations.- C1-co_niteness and fusion products of vertex operator algebras.