Related papers: Composite operators from the operator product expa…
We consider the short-distance behaviour of the product of the Noether O(N) currents in the lattice nonlinear sigma-model. We compare the numerical results with the predictions of the operator product expansion, using one-loop perturbative…
In logarithmic conformal field theory, primary fields come together with logarithmic partner fields on which the stress-energy tensor acts non-diagonally. Exploiting this fact and global conformal invariance of two- and three-point…
It has been recently proposed to use the operator product expansion to evaluate the expectation values of renormalized operators without the need of a direct computation of the relevant renormalization constants. We test the viability of…
Non-perturbative renormalization of lattice composite operators plays a crucial role in many applications of lattice field theory. We sketch the general problems involved in this task and the methods which are currently used to cope with…
We propose a new locally smeared operator product expansion to decompose nonlocal operators in terms of a basis of smeared operators. The smeared operator product expansion formally connects nonperturbative matrix elements determined…
A new method for calculating the coefficient functions of the operator product expansion is proposed which does not depend explicitly on elementary fields. Coefficient functions are defined entirely in terms of composite operators. The…
The short-distance singularity of the product of a composite scalar field that deforms a field theory and an arbitrary composite field can be expressed geometrically by the beta functions, anomalous dimensions, and a connection on the…
We investigate the Operator Product Expansion (OPE) on the lattice by directly measuring the product <Jmu Jnu> (where J is the vector current) and comparing it with the expectation values of bilinear operators. This will determine the…
We propose an operator product expansion for planar form factors of local operators in $\mathcal{N}=4$ SYM theory. This expansion is based on the dual conformal symmetry of these objects or, equivalently, the conformal symmetry of their…
The paper presents a model-independent, nonperturbative proof of operator product expansions in quantum field theory. As an input, a recently proposed phase space condition is used that allows a precise description of point field…
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…
We propose a new method for computing the renormalization functions, which is based on the ideas of operator product expansion and large momentum expansion. In this method, the renormalization $Z$-factors are determined by the ultraviolet…
We propose a variational method for identifying lattice operators in a critical quantum spin chain with scaling operators in the underlying conformal field theory (CFT). In particular, this allows us to build a lattice version of the…
These proceedings review recent work on hyperasymptotic constructions to the operator product expansion. Quantities we consider are the static potential and the pole mass.
We give an introduction to the Mathematica package Lambda, designed for calculating $\lambda$-brackets in both vertex algebras, and in SUSY vertex algebras. This is equivalent to calculating operator product expansions in two-dimensional…
In the conformal field theories having affine SL(2) symmetry, we study the operator product expansion (OPE) involving primary fields in highest weight representations. For this purpose, we analyze properties of primary fields with definite…
We consider the critical relaxation of the Ising model, the so-called model A, and study its operator product expansion. Within perturbation theory, we focus on the operator product expansions of the two-point function and the response…
The generic structure of 1-, 2- and 3-point functions of fields residing in indecomposable representations of arbitrary rank are given. These in turn determine the structure of the operator product expansion in logarithmic conformal field…
Despite recent advances in the lattice representation theory of (generalized) symmetries, many simple quantum spin chains of physical interest are not included in the rigid framework of fusion categories and weak Hopf algebras. We…
The most general operator product expansion in conformal field theory is obtained using the embedding space formalism and a new uplift for general quasi-primary operators. The uplift introduced here, based on quasi-primary operators with…