Related papers: Conformal Field Theory, Tensor Categories and Oper…
Several aspects of fusion rings and fusion rule algebras, and of their manifestations in twodimensional (conformal) field theory, are described: diagonalization and the connection with modular invariance; the presentation in terms of…
This is a continuation of the paper "Modular tensor categories and orbifold theories", arXiv:math.QA/0104242. It discusses orbifold models of conformal filed theory, or, in mathematical language, question of constructing the category of…
Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…
This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…
Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.
In these proceedings we summarize previous work where we formalize a general concept of algebraic field theories using operads. After giving a gentle reminder of algebraic quantum field theory, operads and their algebras, we construct field…
We investigate some aspects of the c=-2 logarithmic conformal field theory. These include the various representations related to this theory, the structures which come out of the Zhu algebra and the W algebra related to this theory. We try…
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…
Topological field theory in three dimensions provides a powerful tool to construct correlation functions and to describe boundary conditions in two-dimensional conformal field theories.
Global conformal invariance determines the form of two and three-point functions of quasi-primary operators in a conformal field theory, and generates nontrivial relations between terms in the operator product expansion. These ideas are…
In a short review of recent work, we discuss the general problem of constructing the actions of new conformal field theories from old conformal field theories. Such a construction follows when the old conformal field theory admits new…
The purpose of this paper is to introduce the cohomology of various algebras over an operad of moduli spaces including the cohomology of conformal field theories (CFT's) and vertex operator algebras (VOA's). This cohomology theory produces…
A field algebra is a ``non-commutative'' generalization of a vertex algebra. In this paper we develop foundations of the theory of field algebras.
A brief overview of the recent developments of operadic and higher categorical techniques in algebraic quantum field theory is given. The relevance of such mathematical structures for the description of gauge theories is discussed.
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
In this note, we observe a relation between dialgebras (in particular, Leibniz algebras) and conformal algebras. The purpose is to show how the methods of conformal algebras help solving problems on dialgebras, and, conversely, how the…
This primer is an introduction to Conformal Field Theory in $D\geq3$. It is designed to introduce the reader to many of the important foundational concepts and methods in CFT. In it, pig picture ideas are prioritized over technical details,…
This is the first part in a two-part series of papers constructing a unitary structure for the modular tensor category (MTC) associated to a unitary rational vertex operator algebra (VOA).
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a…
The algebraic structures related with integrable structure of superconformal field theory (SCFT) are introduced. The SCFT counterparts of Baxter's Q-operator are constructed. The fusion-like relations for the transfer-matrices in different…