Related papers: On bosonization of 2d conformal field theories
We utilise bosonic Fock spaces, considered as Virasoro modules, to make free field realisations of the so-called staggered modules of two-dimensional logarithmic conformal field theories. A general formula for the $\beta$-invariant of a…
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 review some aspects of the free field approach to two-dimensional conformal field theories. Specifically, we discuss the construction of free field resolutions for the integrable highest weight modules of untwisted affine Kac-Moody…
We give an explicit description of "bundles of conformal blocks" in Wess-Zumino-Witten models of Conformal field theory and prove that integral representations of Knizhnik-Zamolodchikov equations constructed earlier by the second and third…
We consider the free field approach or bosonization technique for the Wess-Zumino-Novikov-Witten model with arbitrary Kac-Moody algebra on Riemann surface of genus zero. This subject was much studied previously, and the paper can be…
The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…
We classify degeneration patterns of Verma modules over the N=2 superconformal algebra in two dimensions. Explicit formulae are given for singular vectors that generate maximal submodules in each of the degenerate cases. The mappings…
We show how to deal with screening charges involving fractional powers of free fields. This enables us to use the free field Wakimoto construction to obtain complete expressions for integral representations of conformal blocks for N-point…
We provide a brief but self-contained review of two-dimensional conformal field theory, from the basic principles to some of the simplest models. From the representations of the Virasoro algebra on the one hand, and the state-field…
Modules over affine Lie superalgebras ${\cal G}$ are studied, in particular, for ${\cal G}=\hat{OSP(1,2)}$. It is shown that on studying Verma modules, much of the results in Kac-Moody algebra can be generalized to the super case. Of most…
We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux $Y(s_1,...,s_k)$ with $k\geq 2$ rows on $d$-dimensional anti-de-Sitter space. Auxiliary…
We show that our construction of boson type realizations of affine $\mathfrak{sl}(n+1)$ in terms of intermediate Wakimoto modules gives representations that are generically isomorphic to certain Verma type modules. We then use this…
We investigate the free fields realization of the twisted Heisenberg-Virasoro algebra $\mathcal{H}$ at level zero. We completely describe the structure of the associated Fock representations. Using vertex-algebraic methods and screening…
A review is presented of the recently obtained expressions for conformal blocks for {\it admissible} representations in $SL(2)$ current algebra based on the Wakimoto free field construction. In this realization one needs to introduce a…
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…
$Vect(N)$, the algebra of vector fields in $N$ dimensions, is studied. Some aspects of local differential geometry are formulated as $Vect(N)$ representation theory. There is a new class of modules, {\it conformal fields}, whose…
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…
The construction of D-branes in N=2 superconformal minimal models, based on free field realization of N=2 super-Virasoro algebra unitary modules is represented.
A discretized massless wave equation in two dimensions, on an appropriately chosen square lattice, exactly reproduces the solutions of the corresponding continuous equations. We show that the reason for this exact solution property is the…