相关论文: Algebraic Coset Conformal field theories
Some mathematical questions relating to Coset Conformal Field Theories (CFT) are considered in the framework of Algebraic Quantum Field Theory as developed previously by us. We consider the issue of fixed point resolution in the diagonal…
Conformal field theories based on $g/u(1)^d$ coset constructions where $g$ is a reductive algebra are studied.It is shown that the theories are equivalent to constrained WZNW models for $g.$ Generators of extended symmetry algebras and…
In hep-th/9506151 we started a programme devoted to the systematic study of the conformal field theories derived from WZW models based on nonreductive Lie groups. In this, the second part, we continue this programme with a look at the N=1…
We analyse the SU(2)_k WZNW models beyond the integrable representations and in particular the case of SU(2)_0. We find that these are good examples of logarithmic conformal field theories as indecomposable representations are naturally…
The Wess-Zumino-Witten (WZW) theory has a global symmetry denoted by $G_L\otimes G_R$. In the standard gauged WZW theory, vector gauge fields (\ie\ with vector gauge couplings) are in the adjoint representation of the subgroup $H \subset…
We study two-dimensional WZW models with target space a nonreductive Lie group. Such models exist whenever the Lie group possesses a bi-invariant metric. We show that such WZW models provide a lagrangian description of the nonreductive…
We introduce a new class of two dimensional conformal field theories by extending Wess-Zumino-Witten (WZW) models to chiral algebras with matrix-valued levels. The new CFTs are based on holomorphic currents with an operator product…
This article reviews some recent progress in our understanding of the structure of Rational Conformal Field Theories, based on ideas that originate for a large part in the work of A. Ocneanu. The consistency conditions that generalize…
Wess-Zumino-Witten (WZW) models are among the most basic and most studied Conformal Field Theories (CFT). They have had a huge influence not only in physics but also in mathematics, in representation theory and geometry. However their…
We study the use of transformers to reconstruct the compositions of tensor products of two-dimensional rational conformal field theories (RCFTs) based on their low-energy spectra. The task is challenging due to its combinatorial nature. The…
We construct a set of non-rational conformal field theories that consist of deformations of Toda field theory for sl(n). Besides conformal invariance, the theories still enjoy a remnant infinite-dimensional affine symmetry. The case n=3 is…
The magic triangle due to Cvitanovi\'c and Deligne--Gross is an extension of the Freudenthal--Tits magic square of semisimple Lie algebras. In this paper, we identify all two-dimensional rational conformal field theories associated to the…
We discuss non-compact WZW sigma models, especially the ones with symmetric space $H^{\bf C}/H$ as the target, for $H$ a compact Lie group. They offer examples of non-rational conformal field theories. We remind their relation to the…
The conformal field theory based on the $g/u(1)^d$ coset construction is treated as the WZNW theory for the affine Lie algebra $\hat g$ with the constrained $\hat u(1)^d$ subalgebra.Using a modification of the generalized canonical…
Exact conformal field theories (CFTs) are obtained by using the approach of Poisson-Lie (PL) T-duality in the presence of spectators. We explicitly construct some non-Abelian T-dual $\sigma$-models (here as the PL T-duality on a…
We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that…
After a brief review of recent rigorous results concerning the representation theory of rational chiral conformal field theories (RCQFTs) we focus on pairs (A,F) of conformal field theories, where F has a finite group G of global symmetries…
The correlators of free four dimensional conformal field theories (CFT4) have been shown to be given by amplitudes in two-dimensional $so(4,2)$ equivariant topological field theories (TFT2), by using a vertex operator formalism for the…
Chiral orbifold models are defined as gauge field theories with a finite gauge group $\Gamma$. We start with a conformal current algebra A associated with a connected compact Lie group G and a negative definite integral invariant bilinear…
We study the occurrence of global gauge anomalies in the coset models of two-dimensional conformal field theory that are based on gauged WZW models. A complete classification of the non-anomalous theories for a wide family of gauged rigid…