Related papers: Coadjoint Orbits and Conformal Field Theory
Starting with conformally covariant correlation functions, a sequence of functional representations of the conformal algebra is constructed. A key step is the introduction of representations which involve an auxiliary functional. It is…
A two-dimensional chiral conformal field theory can be viewed mathematically as the representation theory of its chiral algebra, a vertex operator algebra. Vertex operator algebras are especially well suited for studying logarithmic…
Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave…
We develop the theory of irregular conformal blocks of the Virasoro algebra. In previous studies, expansions of irregular conformal blocks at regular singular points were obtained as degeneration limits of regular conformal blocks; however,…
In this article an interpretation and a proof of some classical \\theorems in analysis on the integration of analytic vectors fields are derived from the algebraic method of realization of bialgebras which are constructed with the data of a…
We propose an extension of the definition of vertex algebras in arbitrary space-time dimensions together with their basic structure theory. An one-to-one correspondence between these vertex algebras and axiomatic quantum field theory (QFT)…
In this paper we consider an axial torsion to build metric-compatible connections in conformal gravity, with gauge potentials; the geometric background is filled with Dirac spinors: scalar fields with suitable potentials are added…
We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential…
We derive correspondences of correlation functions among dual conformal field theories in two dimensions by developing a "first order formulation" of coset models. We examine several examples, and the most fundamental one may be a…
The main properties of indefinite Kac-Moody and Borcherds algebras, considered in a unified way as Lorentzian algebras, are reviewed. The connection with the conformal field theory of the vertex operator construction is discussed. By the…
This is a review of irrational conformal field theory, which includes rational conformal field theory as a small subspace. Central topics of the review include the Virasoro master equation, its solutions and the dynamics of irrational…
We develop methods for computation of Poisson vertex algebra cohomology. This cohomology is computed for the free bosonic and fermionic Poisson vertex (super)algebras, as well as for the universal affine and Virasoro Poisson vertex…
A solution to the long-standing problem of identifying the conformal field theory governing the transition between quantized Hall plateaus of a disordered noninteracting 2d electron gas, is proposed. The theory is a nonlinear sigma model…
Conformal nets provides a mathematical model for conformal field theory. We define a notion of defect between conformal nets, formalizing the idea of an interaction between two conformal field theories. We introduce an operation of fusion…
The vertex operator algebras and modules associated to the highest weight modules for the Virasoro algebra over an arbitrary field F whose characteristic is not equal to 2 are studied. The irreducible modules of vertex operator algebra…
We develop the notion of a (pro-) conformal pseudo operad and apply it to the construction of the basic cohomology complex of a vertex algebra. The paper heavily uses the ideas and constructions of the work of Tamarkin [Tam02]
I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3) solutions to the WDVV equations of topological…
The correlators of free four dimensional conformal field theories (CFT4) have been shown to be given by amplitudes in two-dimensional $so(4,2)$ equivariant topological field theories (TFT2), by using a vertex operator formalism for the…
In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an…
Given a vertex operator algebra V , one can attach a graded Poisson algebra called the C2-algebra R(V). The associate Poisson scheme provides an important invariant for V and has been studied by Arakawa as the associated variety. In this…