Related papers: Fusion and singular vectors in A1{(1)} highest wei…
Using Jakobsen theorems, unitarizability in Hermitian Symmetric Spaces is discussed. The set of all missing highest weights is explicitly calculated and the construction of their corresponding highest weights vectors is studied.
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…
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…
We study various aspects of parafermionic theories such as the precise field content, a description of a basis of states (that is, the counting of independent states in a freely generated highest-weight module) and the explicit expression…
The problem of describing the singular vectors of $\cW_3$ and $\cW_3^{(2)}$ Verma modules is addressed, viewing these algebras as BRST quantized Drinfeld-Sokolov (DS) reductions of $A^{(1)}_2\,$. Singular vectors of an $A^{(1)}_2\,$ Verma…
Equations are found for exact g-functions corresponding to integrable bulk and boundary flows between successive unitary c<1 minimal conformal field theories in two dimensions, confirming and extending previous perturbative results. These…
This article is the second chapter of a two-part series dedicated to the mathematical study of the higher-spin symmetry enjoyed by the $\mathfrak{sl}_3$ boundary Toda Conformal Field Theory. Namely, based on a probabilistic definition of…
By interpreting the fusion matrix as an adjacency matrix we associate a loop model to every primary operator of a generic conformal field theory. The weight of these loop models is given by the quantum dimension of the corresponding primary…
We investigate a one-point restriction of conformal blocks on $(\mathbb{P}^1,\infty,1,0)$ associated with modules over a vertex operator algebra. By restricting the module attached to the point $\infty$ to its bottom degree, we obtain a new…
We present some new exact results for general four-dimensional superconformal field theories. We derive differential equations governing the coupling constant dependence of chiral primary correlators. For N=2 theories we show that the…
We derive a set of recursion formulae to construct singular vectors for the $N=2$ (untwisted) algebra, by using the approach of Bauer, di Francesco, Itzykson and Zuber. Applying these formulae, we obtain explicit expressions for the charged…
The main purpose of this work is to review the results obtained recently concerning the unitarization of highest weight representations for affine Kac-Moody algebras following the work of Jakobsen and Kac.
The BRST quantisation of the Drinfeld - Sokolov reduction applied to the case of $A^{(1)}_2\,$ is explored to construct in an unified and systematic way the general singular vectors in ${\cal W}_3$ and ${\cal W}_3^{(2)}$ Verma modules. The…
N=2 noncritical strings are closely related to the $\Slr/\Slr$ Wess-Zumino- Novikov-Witten model, and there is much hope to further probe the former by using the algebraic apparatus provided by the latter. An important ingredient is the…
We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors in the GL(3)-based quantum integrable…
We define a new modular functor based on Kac-Wakimoto admissible representations and the corresponding D-module on the moduli space of rank 2 vector bundles with parabolic structure. A new fusion functor arises which is related to…
A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an abelian ideal. When the superalgebra is of affine Kac-Moody type, a generalisation of…
We construct a realistic field-theoretic model for the structure of a heavy meson in the heavy quark limit. The model is fully covariant and satisfies heavy quark symmetry. The Isgur-Wise function, the decay constant, and the axial vector…
In this paper we extend our previous results concerning Jackson integral solutions of the boundary quantum Knizhnik-Zamolodchikov equations with diagonal K-operators to higher-spin representations of quantum affine $\mathfrak{sl}_2$. First…
In this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated. These theories are realized in terms of free scalar fields starting from the simple $b-c$ systems and scalar fields on…