Related papers: Classification of operator algebraic conformal fie…
Conformal field theory and its axiomatisation in terms of vertex operator algebras or chiral algebras are most commonly considered on the Riemann sphere. However, an important constraint in physics and an interesting source of mathematics…
Short distance scaling limits of a class of integrable models on two-dimensional Minkowski space are considered in the algebraic framework of quantum field theory. Making use of the wedge-local quantum fields generating these models, it is…
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 introduce a three-dimensional quantum field theory with an infinite-dimensional symmetry, realized explicitly through a centrally extended affine graded Lie algebra. This symmetry is a direct three-dimensional generalization of the…
In this short note, we classify linear categorified open topological field theories in dimension two by pivotal Grothendieck-Verdier categories, a type of monoidal category equipped with a weak, not necessarily rigid duality. In combination…
Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…
In this paper, we study the Carrollian and Galilean conformal field theories (CCFT and GCFT) in $d>2$ dimensions. We construct the highest weight representations (HWR) of Carrollian and Galilean conformal algebra (CCA and GCA). Even though…
We review various aspects of $\cW$-algebra symmetry in two-dimensional conformal field theory and string theory. We pay particular attention to the construction of $\cW$-algebras through the quantum Drinfeld-Sokolov reduction and through…
We construct symmetry generators and operators for $J\bar{T}$-deformed conformal field theories by generalizing the framework established for $T\bar{T}$ deformations. Working in the Hamiltonian formalism on the plane, we derive the symmetry…
It is well known that a local, unitary Poincare-invariant 2D QFT with a global scaling symmetry and a discrete non-negative spectrum of scaling dimensions necessarily has both a left and a right local conformal symmetry. In this paper we…
Two dimensional conformal field theories with central charge one are discussed. After a short review of theories based on one free boson, a different CFT is described, which is obtained as a limit of minimal models.
Neural Network Field Theories (NN-FTs) represent a novel construction of arbitrary field theories, including those of conformal fields, through the specification of the network architecture and prior distribution for the network parameters.…
This is a set of introductory lecture notes on conformal field theory. Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. It begins with a…
We generalize, to any space-time dimension, the unitarity bounds of highest weight UIR's of the conformal groups with Lie algebras $so(2,d)$. We classify gauge theories invariant under $so(2,d)$, both integral and half-integral spins. A…
We consider the two-dimensional $\mathfrak{sl}_n$ quantum Toda field theory with an imaginary background charge. This conformal field theory has a higher spin symmetry ($W_n$ algebra), a central charge $c \leq n-1$ and a continuous…
For a (finite-dimensional) real Hilbert space $\mathfrak h$ and an orthogonal projection $p$, we consider the associated Heisenberg Lie algebra and the two-dimensional Heisenberg conformal net. Given an even lattice $Q$ in $\mathfrak h$…
We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer…
We consider a class of non-unitary Toda theories based on the Lie superalgebras $A^{(1)}(n,n)$ in two-dimensional Minkowski spacetime, which can be twisted into a topological sector. In particular we study the simplest example with $n=1$…
We attempt a direct derivation of a conformal field theory description of 2D quantum gravity~+~matter from the formalism of integrable hierarchies subjected to Virasoro constraints. The construction is based on a generalization of the…
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…