Related papers: Code conformal field theory and framed algebra
We review how modular categories, and commutative and non-commutative Frobenius algebras arise in rational conformal field theory. For Euclidean CFT we use an approach based on sewing of surfaces, and in the Minkowskian case we describe CFT…
Recently (hep-th/9307183) we showed that for the case of the WZW- and the minimal models fusion can be understood as a certain ring-like tensor product of the symmetry algebra. In this paper we generalize this analysis to arbitrary chiral…
The role of automorphisms of infinite-dimensional Lie algebras in conformal field theory is examined. Two main types of applications are discussed; they are related to the enhancement and reduction of symmetry, respectively. The structures…
We classify a one-parameter family, $\mathfrak{confcarr}_z(d+1)$, of conformal extensions of the Carroll algebra in arbitrary dimension with $z$ being the anisotropic scaling exponent. We further obtain their infinite-dimensional…
Conformal symmetries appear in many parts of physics and play a unique role in exploring the Universe. In this work, we consider the possibility of constructing conformal theories of gravity in the Symmetric Teleparallel Gravity framework,…
In this paper, we introduce a finite Lie conformal superalgebra called the Heisenberg-Virasoro Lie conformal superalgebra $\mathfrak{s}$ by using a class of Heisenberg-Virasoro Lie conformal modules. The super Heisenberg-Virasoro algebra of…
The conformal bootstrap hypothesis is a powerful idea in theoretical physics which has led to spectacular predictions in the context of critical phenomena. It postulates an explicit expression for the correlation functions of a conformal…
We explore new connections between the fields and local observables in two dimensional chiral conformal field theory. We show that in a broad class of examples, the von Neumann algebras of local observables (a conformal net) can be obtained…
The loop super-Virasoro conformal superalgebra $\mathfrak{cls}$ associated with the loop super-Virasoro algebra is constructed in the present paper. The conformal superderivation algebra of $\mathfrak{cls}$ is completely determined, which…
We introduce the notion of a conformal design based on a vertex operator algebra. This notation is a natural analog of the notion of block designs or spherical designs when the elements of the design are based on self-orthogonal binary…
Neural Network Field Theories (NN-FTs) typically describe Generalized Free Fields that lack a local stress-energy tensor in two dimensions, obstructing the realization of Virasoro symmetry. We present the ``Log-Kernel'' (LK) architecture,…
In this paper, we introduce a class of infinite Lie conformal algebras $\mathfrak{B}(\alpha,\beta,p)$, which are the semi-direct sums of Block type Lie conformal algebra $\mathfrak{B}(p)$ and its non-trivial conformal modules of $\Z$-graded…
We prove a finite torsion-free associative conformal algebra to have a finite faithful conformal representation. As a corollary, it is shown that one may join a conformal unit to such an algebra. Some examples are stated to demonstrate that…
We review the main topics concerning Fusion Rule Algebras (FRA) of Rational Conformal Field Theories. After an exposition of their general properties, we examine known results on the complete classification for low number of fields ($\leq…
We revisit the construction of conformal field theories based on Takiff algebras and superalgebras that was introduced by Babichenko and Ridout. Takiff superalgebras can be thought of as truncated current superalgebras with Z-grading which…
We demonstrate that certain Virasoro characters (and their linear combinations) in minimal and non-minimal conformal models which admit factorized forms are manifestly related to the ADE series. This permits to extract quasi-particle…
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…
This Letter initiates the study of what we call non-chiral staggered Virasoro modules, indecomposable modules on which two copies of the Virasoro algebra act with the two zero-modes acting non-semisimply. This is motivated by the "puzzle"…
We discuss the problem to develop a mathematical theory of a certain class of nonrational conformal field theories (CFT) which contain the unitary CFT. A variant of the concept of a modular functor is proposed that appears to be suitable…
There exists two types of nonassociative algebras whose associator satisfies a symmetric relation associated with a 1-dimensional invariant vector space with respect to the natural action of the symmetric group on three elements. The first…