相关论文: Algebraic K-Theory and Partition Functions in Conf…
Affine Kac-Moody algebras give rise to interesting systems of differential equations, so-called Knizhnik-Zamolodchikov equations. The monodromy properties of their solutions can be encoded in the structure of a modular tensor category on (a…
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…
When is a $q$-series modular? This is an interesting open question in mathematics that has deep connections to conformal field theory. In this paper we define a particular $r$-fold $q$-hypergeometric series $f_{A,B,C}$, with data given by a…
We argue that rational conformally invariant quantum field theories in two dimensions are closely related to torsion elements of the algebraic K-theory group K_3(C). If such a theory has an integrable matrix perturbation with purely elastic…
We review how modular categories, and commutative and non-commutative Frobenius algebras arise in rational conformal field theory. For Euclidean CFT we use an approach based on sewing of surfaces, and in the Minkowskian case we describe CFT…
We derive new closed form expressions for the partition functions of free conformally-coupled scalars on $S^{2D-1}\times S^1$ which resum the exact high-temperature expansion. The derivation relies on an identification of the partition…
Let $C$ be a symmetrizable generalized Cartan Matrix, and $q$ an indeterminate. ${\fg}(C)$ is the Kac-Moody Lie algebra and $U=U_q({\fg}(C))$ the associated quantum enveloping algebra over $ k={\Bbb Q}(q)$. The quantum function algebra…
Study of the matrix-level affine algebra $U_{m,K}$ is motivated by conformal field theory and the fractional quantum Hall effect. Gannon completed the classification of $U_{m,K}$ modular-invariant partition functions. Here we connect the…
The most basic structure of chiral conformal field theory (CFT) is the Verlinde ring. Freed-Hopkins-Teleman have expressed the Verlinde ring for the CFT's associated to loop groups, as twisted equivariant K-theory. We build on their work to…
In 2D conformal quantum field theory, we continue a systematic study of W-algebras with two and three generators and their highest weight representations focussing mainly on rational models. We review the known facts about rational models…
We examine general aspects of parity functions arising in rational conformal field theories, as a result of Galois theoretic properties of modular transformations. We focus more specifically on parity functions associated with affine Lie…
A constructive procedure is proposed for formulation of linear differential equations invariant under global symmetry transformations forming a semi-simple Lie algebra f. Under certain conditions f-invariant systems of differential…
Logarithmic conformal field theories are based on vertex algebras with non-semisimple representation categories. While examples of such theories have been known for more than 25 years, some crucial aspects of local logarithmic CFTs have…
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 investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational,…
A concise review of the notions of elliptic functions, modular forms, and theta-functions is provided, devoting most of the paper to applications to Conformal Field Theory (CFT), introduced within the axiomatic framework of quantum field…
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…
Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
The relation between the Seiberg-Witten prepotentials, Nekrasov functions and matrix models is discussed. We derive quasiclassically the matrix models of Eguchi-Yang type, describing the instantonic contribution to the deformed partition…