Related papers: Fusion in coset CFT from admissible singular-vecto…
The fusion rings of Wess-Zumino-Witten models are re-examined. Attention is drawn to the difference between fusion rings over Z (which are often of greater importance in applications) and fusion algebras over C. Complete proofs are given…
We calculate fusion rules for the admissible representations of the affine superalgebra sl(2|1;C) at fractional level k=-1/2 in the Ramond sector. By representing 3-point correlation functions involving a singular vector as the action of…
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 show that the WZW fusion rings at finite levels form a projective system with respect to the partial ordering provided by divisibility of the height, i.e. the level shifted by a constant. From this projective system we obtain WZW fusion…
Modular invariants satisfy remarkable fusion rules. Let $Z$ be a modular invariant associated to a braided subfactor $N\subset M$. The decomposition of the non-normalized modular invariants $Z Z^{*}$ and $Z^{*}Z$ into sums of normalized…
A formula is derived for the fixed point resolution matrices of simple current extended WZW-models and coset conformal field theories. Unlike the analogous matrices for unextended WZW-models, these matrices are in general not symmetric, and…
We examine the so(2,D-1) WZW model at the subcritical level -(D-3)/2. It has a singular vacuum vector at Virasoro level 2. Its decoupling constitutes an affine extension of the equation of motion of the (D+1)-dimensional conformal particle,…
We study the structure of fusion rules for the triplet $W$-algebra $\mathcal{W}_{p_+,p_-}$. By using the vertex tensor category theory developed by Huang, Lepowsky and Zhang, we rederive certain non-semisimple fusion rules given by…
We revisit the problem of performing conformal block decomposition of exchange Witten diagrams in the crossed channel. Using properties of conformal blocks and Witten diagrams, we discover infinitely many linear relations among the crossed…
We derive higher Wess--Zumino--Witten (WZW) and gauged WZW (gWZW) terms within strict higher Chern--Simons (CS) gauge theory. Starting from the Cartan homotopy formula, we obtain the $(2n+2)$-dimensional higher CS forms and transgression…
Gauged Wess-Zumino-Witten theory for compact groups is considered. It is shown that this theory has fermionic BRST-like symmetry and may be exactly solved using localization approach. As an example we calculate functional integral for the…
The quantisation of the Wess-Zumino-Witten model on a circle is discussed in the case of $SU(N)$ at level $k$. The quantum commutation of the chiral vertex operators is described by an exchange relation with a braiding matrix, $Q$. Using…
A powerful approach to the celebrated Wess-Zumino-Witten (WZW) model is provided by its free-field realization. However, explicit calculations of conformal blocks are not described in the literature in full detail. We begin this study with…
The two-character level-1 WZW models corresponding to Lie algebras in the Cvitanovi\'c-Deligne series $A_1,A_2,G_2,D_4,F_4,E_6,E_7$ have been argued to form coset pairs with respect to the meromorphic $E_{8,1}$ CFT. Evidence for this has…
We derive the current algebra of principal chiral models with a Wess-Zumino term. At the critical coupling where the model becomes conformally invariant (Wess-Zumino-Novikov-Witten theory), this algebra reduces to two commuting Kac-Moody…
We study a canonical quantization of the Wess--Zumino--Witten (WZW) model which depends on two integer parameters rather than one. The usual theory can be obtained as a contraction, in which our two parameters go to infinity keeping the…
Two different approaches to calculate the fusion rules of the c_{p,1} series of logarithmic conformal field theories are discussed. Both are based on the modular transformation properties of a basis of chiral vacuum torus amplitudes, which…
Gauging a finite group 0-form symmetry $G$ of a quantum field theory (QFT) results in a QFT with a Rep$(G)$ symmetry implemented by Wilson lines. The group $G$ determines the fusion of Wilson lines. However, in general, the fusion rules of…
We present an analysis of the canonical structure of the WZW theory with untwisted conformal boundary conditions. The phase space of the boundary theory on a strip is shown to coincide with the phase space of the Chern-Simons theory on a…
We propose a systematic method to extract conformal loop models for rational conformal field theories (CFT). Method is based on defining an ADE model for boundary primary operators by using the fusion matrices of these operators as…