Related papers: Operator Product Expansion in Logarithmic Conforma…
Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. We review some main convergence results, conjectures and problems in the construction and study of…
We consider a recursive scheme for defining the coefficients in the operator product expansion (OPE) of an arbitrary number of composite operators in the context of perturbative, Euclidean quantum field theory in four dimensions. Our…
We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean $\varphi^{4}$-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of…
We study the operator product expansions in the chiral algebra $\mathcal{W}_{\infty}$, first using the associativity conditions in the basis of primary generating fields and second using a different basis coming from the free field…
We calculate boundary operator product expansion coefficients for boundary operators in the first column of the Kac table in conformal field theories. For c=0 we give closed form expressions for all such coefficients. Then we generalize to…
We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…
Motivated by the mixing of UV and IR effects, we test the OPE formula in noncommutative field theory. First we look at the renormalization of local composite operators, identifying some of their characteristic IR/UV singularities. Then we…
In this paper we consider logarithmic operators in two different contexts: the adapted to (continuous) Schr\"odinger operators and the classical discrete setting. The Schr\"odinger operator $\mathcal L_V$ on $\mathbb R^d$ is defined as…
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…
We discuss the general covariance of operator product expansion in D-dimensional Euclidean conformal field theories. We propose to organise the expansion in powers of geodesic distance between two insertion points and to use the tangent…
We study non-relativistic conformal field theory on a flat space in the presence of a planar boundary. We compute correlation functions of primary operators and obtain the expression for the boundary conformal block. We also discuss the…
Twisted modules over vertex algebras formalize the relations among twisted vertex operators and have applications to conformal field theory and representation theory. A recent generalization, called twisted logarithmic module, involves the…
We compute, to the first non-trivial order in the $\epsilon$-expansion of a perturbed scalar field theory, the anomalous dimensions of an infinite class of primary operators with arbitrary spin $\ell=0,1,..$, including as a particular case…
We study five-point correlation functions of scalar operators in d-dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing…
We consider correlation functions of operators and the operator product expansion in two-dimensional quantum gravity. First we introduce correlation functions with geodesic distances between operators kept fixed. Next by making two of the…
We show, within the framework of the Euclidean $\phi^4$-quantum field theory in four dimensions, that the Wilson operator product expansion (OPE) is not only an asymptotic expansion at short distances as previously believed, but even…
We establish a direct connection between two fundamental topics: one in probability theory and one in quantum field theory. The first topic is the problem of pointwise multiplication of random Schwartz distributions which has been the…
We describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced in previous work. To take maximal advantage of the known properties of the scalar conformal blocks for…
Amongst conformal field theories, there exist logarithmic conformal field theories such as $c_{p,1}$ models. We have investigated $c_{p,q}$ models with a boundary in search of logarithmic theories and have found logarithmic solutions of…
We derive a nonperturbative, convergent operator product expansion (OPE) for null-integrated operators on the same null plane in a CFT. The objects appearing in the expansion are light-ray operators, whose matrix elements can be computed by…