Related papers: Conformal characters and the modular representatio…
In this work we revisit the "holomorphic modular bootstrap", i.e. the classification of rational conformal field theories via an analysis of the modular differential equations satisfied by their characters. By making use of the…
A comprehensive introduction to two-dimensional conformal field theory is given.
We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of…
Let G be a semisimple group over an algebraically closed field of characteristic p>0. We give a (partly conjectural) simple, closed formula for the character of many indecomposable tilting rational G-modules, assuming that p is large.
We characterize groups with Guoliang Yu's property A (i.e., exact groups) by the existence of a family of uniformly bounded representations which approximate the trivial representation.
The congruence subgroup property is established for the modular representations associated to any modular tensor category. This result is used to prove that the kernel of the representation of the modular group on the conformal blocks of…
Picard groups of tensor categories play an important role in rational conformal field theory. The Picard group of the representation category C of a rational vertex algebra can be used to construct examples of (symmetric special) Frobenius…
We study replication identities satisfied by conformal characters of a 2D CFT, providing a natural framework for a physics interpretation of the famous Hauptmodul property of Monstrous Moonshine, and illustrate the underlying ideas in…
We give several formulas for the character of an arbitrary irreducible finite--dimensional representation for the Yangian of sl_2.
Using the representation theory of the subgroups SL_2(Z_p) of the modular group we investigate the induced fusion algebras in some simple examples. Only some of these representations lead to 'good' fusion algebras. Furthermore, the…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
These pedagogical lectures present some material, classical or more recent, on (Rational) Conformal Field Theories and their general setting ``in the bulk'' or in the presence of a boundary. Two well posed problems are the classification of…
Using computational methods, we complete the determination of the $3$-modular character table of the Chevalley group $F_4(2)$ and its covering group.
This paper studies the Yang-Lee edge singularity of 2-dimensional (2D) Ising model based on a quantum spin chain and transfer matrix measurements on the cylinder. Based on finite-size scaling, the low-lying excitation spectrum is found at…
In this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated. These theories are realized in terms of free scalar fields starting from the simple $b-c$ systems and scalar fields on…
This is a review of two-dimensional conformal field theory including some of the relations to integrable models. An effort is made to develop the basic formalism in a way which is as elementary and flexible as possible at the same time.…
The two pillars of rational conformal field theory and rational vertex operator algebras are modularity of characters on the one hand and its interpretation of modules as objects in a modular tensor category on the other one. Overarching…
The representation theory of semisimple algebraic groups over the complex numbers (equivalently, semisimple complex Lie algebras or Lie groups, or real compact Lie groups) and the question of whether a given representation is symplectic or…
The fusion rules and modular matrix of a rational conformal field theory obey a list of properties. We use these properties to classify rational conformal field theories with not more than six primary fields and small values of the fusion…
In view of applications to conformal field theory or to other branches of theoretical physics and mathematics, new examples of character tables for Drinfeld doubles of finite groups (modular data) are made available on a website.