Related papers: Conformal Blocks and Correlators in WZNW Model. I.…
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 invistigate exact solutions for the two-dimensional quantum field theories called Wess-Zumino-Novikov-Witten (WZNW) models. A WZNW model is a sigma model whose classical fields are applications from a bidimensional space-time (a Riemann…
Correlation functions of primary fields in the Wess-Zumino-Novikov-Witten (WZNW) model are known to satisfy a system of Knizhnik-Zamolodchikov (KZ) equations, which involve constants of motion of the exactly-solvable Gaudin magnet. We…
This paper continues the same-named article, Part I (math.QA/9812083). We give a global operator approach to the WZWN theory for compact Riemann surfaces of an arbitrary genus g with marked points. Globality means here that we use…
We survey some recent work on conformal blocks in genus zero, focussing on (1) Chern classes, global generation and morphisms, and (2) the Knizhnik--Zamolodchikov connection on conformal blocks (and invariants), their motivic realizations,…
We show how bosonic (free field) representations for so-called degenerate conformal theories are built by singular vectors in Verma modules. Based on this construction, general expressions of conformal blocks are proposed. As an example we…
Extending our earlier work on PSL(2|2), we explain how to reduce the solution of WZNW models on general type I supergroups to those defined on the bosonic subgroup. The new analysis covers in particular the supergroups GL(M|N) along with…
The gauged SL(2,R)/U(1) Wess-Zumino-Novikov-Witten (WZNW) model is classically an integrable conformal field theory. We have found a Lax pair representation for the non-linear equations of motion, and a B"acklund transformation. A…
The chiral Wess-Zumino-Novikov-Witten (WZNW) model provides the simplest class of rational conformal field theories which exhibit a non-abelian braid-group statistics and an associated "quantum symmetry". The canonical derivation of the…
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 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…
In the spirit of the quantum Hamiltonian reduction we establish a relation between the chiral $n$-point functions, as well as the equations governing them, of the $A_1^{(1)}$ WZNW conformal theory and the corresponding Virasoro minimal…
We investigate the W-algebras generated by the integer dimension chiral primary operators of the SU(2)_0 WZNW model. These have a form almost identical to that found in the c=-2 model but have, in addition, an extended Kac-Moody structure.…
We derive explicit expressions for the conformal blocks of the Ising conformal field theory, for the correlators of an arbitrary number of primary fields. These results are obtained from the bosonized description of the Ising model.…
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…
Elements of a global operator approach to the WZWN theory for compact Riemann surfaces of arbitrary genus $g$ are given. Sheaves of representations of affine Krichever-Novikov algebras over a dense open subset of the moduli space of Riemann…
The $GL(1|1)$ WZW model in the free field realization that uses the $bc$ system is revisited. By bosonizing the $bc$ system we describe the Neveu--Schwarz and Ramond sector modules $\mathcal V^{\text{NS}}_{en}=\bigoplus_{l\in\mathbb…
We use the embedding formalism to construct conformal fields in $D$ dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in $(D+2)$ dimensions to the projective null cone. Conformal correlators may be…
The structure of Hamiltonian reductions of the Wess-Zumino-Novikov-Witten (WZNW) theory by first class Kac-Moody constraints is analyzed in detail. Lie algebraic conditions are given for ensuring the presence of exact integrability,…
We consider the Hamiltonian reduction of the two-loop Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra $\cgh$. The resulting reduced models, called {\em Generalized Non-Abelian Conformal Affine Toda…