相关论文: Modular data: the algebraic combinatorics of confo…

This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…

Conformal field theory (CFT) in two dimensions provide a rich source of subfactors. The fact that there are so many subfactors coming from CFT have led people to conjecture that perhaps all finite depth subfactors are related to CFT. In…

We consider those two-dimensional rational conformal field theories (RCFTs) whose chiral algebras, when maximally extended, are isomorphic to the current algebra formed from some affine non-twisted Kac--Moody algebra at fixed level. In this…

Recently, additive combinatorics has blossomed into a vibrant area in mathematical sciences. But it seems to be a difficult area to define - perhaps because of a blend of ideas and techniques from several seemingly unrelated contexts which…

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…

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

In these notes, based on lectures given in Istanbul, we give an introduction both to Monstrous Moonshine and to the classification of rational conformal field theories, using this as an excuse to explore several related structures and go on…

This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.

We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories.…

We present recent progress in theory of local conformal nets which is an operator algebraic approach to study chiral conformal field theory. We emphasize representation theoretic aspects and relations to theory of vertex operator algebras…

Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our…

Conformal field theory (CFT) has become an active area of research beyond its origins in statistical physics and attracted much attention due to its intrinsic mathematical interest, which reveals deep connections with other diverse branches…

A comprehensive introduction to logarithmic conformal field theory, using an algebraic point of view, is given. A number of examples are explained in detail, including the c=-2 triplet theory and the k=-4/3 affine su(2) theory. We also give…

A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…

Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory. This is a review of recent developments in the subject.

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…

Certain integrable models are described by pairs (X,Y) of ADET Dynkin diagrams. At high energy these models are expected to have a conformally invariant limit. The S-matrix of the model determines algebraic equations, whose solutions are…

CFTs are naturally defined on Riemann surfaces. The rational ones can be solved using methods from algebraic geometry. One particular feature is the covariance of the partition function under the mapping class group. In genus $g=1$, this…

In this letter we present some new results on modular theory and its application in quantum field theory. In doing this we develop some new proposals how to generalize concepts of geometrical action. Therefore the spirit of this letter is…

We review the main topics concerning Fusion Rule Algebras (FRA) of Rational Conformal Field Theories. After an exposition of their general properties, we examine known results on the complete classification for low number of fields ($\leq…