Related papers: Fusion in the W_3 algebra
We define and calculate the fusion algebra of WZW model at a rational level by cohomological methods. As a byproduct we obtain a cohomological characterization of admissible representations of $\widehat{\gtsl}_{2}$.
Fusion is defined for arbitrary lowest weight representations of $W$-algebras, without assuming rationality. Explicit algorithms are given. A category of quasirational representations is defined and shown to be stable under fusion.…
Recently (hep-th/9307183) we showed that for the case of the WZW- and the minimal models fusion can be understood as a certain ring-like tensor product of the symmetry algebra. In this paper we generalize this analysis to arbitrary chiral…
We use recently derived explicit formulae for the Virasoro algebra's singular vectors to give constructive proofs of three results due to Feigin and Fuchs. The main result, which is needed for a rigorous treatment of fusion, describes the…
These lecture notes are a brief introduction to Wess-Zumino-Witten models, and their current algebras, the affine Kac-Moody algebras. After reviewing the general background, we focus on the application of representation theory to the…
We present the first polytope volume formulas for the multiplicities of affine fusion, the fusion in Wess-Zumino-Witten conformal field theories, for example. Thus, we characterise fusion multiplicities as discretised volumes of certain…
Finite versions of W-algebras are introduced by considering (symplectic) reductions of finite dimensional simple Lie algebras. In particular a finite analogue of $W^{(2)}_3$ is introduced and studied in detail. Its unitary and non-unitary,…
We derive the fusion rules for a basic series of admissible representations of $\hat{sl}(3)$ at fractional level $3/p-3$. The formulae admit an interpretation in terms of the affine Weyl group introduced by Kac and Wakimoto. It replaces the…
Fusion of positive energy representations is defined using Connes' tensor product for bimodules over a von Neumann algebra. Fusion is computed using the analytic theory of primary fields and explicit solutions of the Knizhnik-Zamolodchikov…
We consider three-point couplings in simple Lie algebras -- singlets in triple tensor products of their integrable highest weight representations. A coupling can be expressed as a linear combination of products of finitely many elementary…
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 study 3d theories determined by three-manifolds. Previously, we found that some basic 3d dualities relate to the surgeries of three-manifolds and defined gauge circles and matter circles. In this note, we discuss some operations…
On the basis of the Schwinger boson representation for the Elliott model developed in (III), the Holstein-Primakoff representation for the su(3)-algebra is presented. The basic idea is the same as that adopted in (II), and as an example,…
The logarithmic triplet model W_2,3 at c=0 is studied. In particular, we determine the fusion rules of the irreducible representations from first principles, and show that there exists a finite set of representations, including all…
We construct new Yang-Baxter integrable boundary conditions in the lattice approach to the logarithmic minimal model WLM(1,p) giving rise to reducible yet indecomposable representations of rank 1 in the continuum scaling limit. We interpret…
We consider the fusion algebras arising in e.g. Wess-Zumino-Witten conformal field theories, affine Kac-Moody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix $S$, we find…
In the first of this two-part series, we find `fixed point factorisation' formulas, towards an understanding of the fusion ring of WZW models. Fixed-point factorisation refers to the simplifications in the data of a CFT involving primary…
In a previous paper we studied ``weakly primitive axial algebras'' with respect to more general fusion rules, for which at least one axis satisfies the fusion rules. In this continuation, a concise description is provided of the…
The logarithmic minimal models are not rational but, in the W-extended picture, they resemble rational conformal field theories. We argue that the W-projective representations are fundamental building blocks in both the boundary and bulk…
We define a Frobenius algebra over fusion categories of the form Rep$(G)\boxtimes$Rep$(G)$ which generalizes the diagonal subgroup of $G\times G$. This allows us to extend field theoretical constructions which depend on the existence of a…