Related papers: Operator algebra of the SL(2) conformal field theo…
In these notes I briefly outline SL(2) degenerate conformal field theories and their application to some related models, namely 2d gravity and N=2 discrete superconformal series.
$sl_2$-covariant expressions for structure constants of the associative algebra of deformed oscillators $Aq\left(2,\nu\right)$ are obtained.
For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the…
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
The free field representation of the osp(1|2) current algebra is analyzed. The four point conformal blocks of the theory are studied. The structure constants for the product of an arbitrary primary operator and a primary field that…
In the conformal field theories having affine SL(2) symmetry, we study the operator product expansion (OPE) involving primary fields in highest weight representations. For this purpose, we analyze properties of primary fields with definite…
A general two dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed subalgebra generated by $(L_{-1}, L_{0},…
We discuss some open problems in a program of constructing and studying two-dimensional conformal field theories using the representation theory of vertex operator algebras.
We study the free field realization of the two-dimensional osp(1|2) current algebra. We consider the case in which the level of the affine osp(1|2) symmetry is a positive integer. Using the Coulomb gas technique we obtain integral…
We implement the O(d,d,Z) transformations of T-duality as automorphisms of the operator algebras of Conformal Field Theories. This extends these transformations to arbitrary field configurations in the deformation class.
We extend SL(2)-orbit theorems for degeneration of mixed Hodge structures to a situation in which we do not assume the polarizability of graded quotients. We also obtain analogous results on Deligne systems.
A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Applying the generators of the closed subalgebra generated by…
This is the seventh article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It discusses an interesting class of observables localised on surfaces that attracts steadily growing attention.…
We review some results recently obtained for the conformal field theories based on the affine Lie superalgebra osp(1|2). In particular, we study the representation theory of the osp(1|2) current algebras and their character formulas. By…
An analytic expression is proposed for the three-point function of the exponential fields in the Liouville field theory on a sphere. In the classical limit it coincides with what the classical Liouville theory predicts. Using this function…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
We present a vertex operator algebra which is an extension of the level $k$ vertex operator algebra for the $\hat{sl}_2$ conformal field theory. We construct monomial basis of its irreducible representations.
For any complex simple Lie algebra, we generalize primary fileds in the Wess-Zumino-Novikov-Witten conformal field theory with respect to the case of irregular singularities and we construct integral representations of hypergeometric…
We describe the construction of the genus-zero parts of conformal field theories in the sense of G. Segal from representations of vertex operator algebras satisfying certain conditions. The construction is divided into four steps and each…
We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are…