Related papers: Matrix model version of AGT conjecture and general…

The connection between Riemann surfaces with boundaries and the theory of vertex operator algebras is discussed in the framework of conformal field theories defined by Kontsevich and Segal and in the framework of their generalizations in…

The singular part of the \textit{operator product expansion} (OPE) of a pair of \textit{globally conformal invariant} (GCI) scalar fields $\phi$ of (integer) dimension $d$ can be written as a sum of the 2-point function of $\phi$ and $d-1$…

We introduce a symmetric operad whose algebras are the Operator Product Expansion (OPE) Algebras of quantum fields. There is a natural classical limit for the algebras over this operad and they are commutative associative algebras with…

We present a new algorithm for the numerical evaluation of five-point conformal blocks in $d$-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in…

Operator product expansions (OPEs) in quantum field theory (QFT) provide an asymptotic relation between products of local fields defined at points $x_1, \dots, x_n$ and local fields at point $y$ in the limit $x_1, \dots, x_n \to y$. They…

We extend the proof from arXiv:1012.3137, which interprets the AGT relation as the Hubbard-Stratonovich duality relation to the case of 5d gauge theories. This involves an additional q-deformation. Not surprisingly, the extension turns out…

The operator product expansion in four-dimensional superconformal field theory is discussed. The OPE takes a particularly simple form for chiral operators, in $N=1$ and $N=2$, and for analytic operators, in $N=2$ and $N=4$. It is argued…

Since the ($\beta$-deformed) hermitian one-matrix models can be represented as the integrated conformal field theory (CFT) expectation values, we construct the operators in terms of the generators of the Heisenberg algebra such that the…

We consider the structure of the operator product expansion (OPE) in conformal field theory by employing the OPE block formalism. The OPE block acted on the vacuum is promoted to an operator and its implications are examined on a non-vacuum…

By using the free field worldsheet realization described by Gaberdiel and Gopakumar recently, we construct the nontrivial lowest generators of the higher spin superalgebra $hs(2,2|4)$. They consist of cubic terms between the bilinears of…

This manuscript explores the connections between a class of stochastic processes called "Stochastic Loewner Evolution" (SLE) and conformal field theory (CFT). First some important results are recalled which we utilise in the sequel, in…

Let $\mathbb V=\bigoplus_{n\in\mathbb N}\mathbb V(n)$ be a $C_2$-cofinite vertex operator algebra. We prove the convergence of Segal's sewing of conformal blocks associated to analytic families of pointed compact Riemann surfaces and…

The Brownian loop soup is a conformally invariant statistical ensemble of random loops in two dimensions characterized by an intensity $\lambda>0$, with central charge $c=2 \lambda$. Recent progress resulted in an analytic form for the…

We investigate the relation between 3d N=2 theories and 2d free field correlators or Dotsenko-Fateev (DF) integrals for Liouville CFT. We show that the S^2xS^1 partition functions of some known 3d Seiberg-like dualities reduce, in a…

We review the algebraic and analytic aspects of the conformal field theory (CFT) and its relation to the stochastic Loewner evolution (SLE) in an example of the Ising model. We obtain the scaling limit of the correlation functions of Ising…

String theory is currently the most promising theory to explain the spectrum of the elementary particles and their interactions. One of its most important features is its large symmetry group, which contains the conformal transformations in…

We reconstruct the whole family of self-adjoint Hamiltonians of Ter-Martirosyan-- Skornyakov type for a system of two identical fermions coupled with a third particle of different nature through an interaction of zero range. We proceed…

We consider all genus two correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially expressed in terms of a sequence of…

Based on prototypical example of Al.Zamolodchikov's recursion relations for the four point conformal block and using recently proposed Alday-Gaiotto-Tachikawa (AGT) conjecture, recursion relations are derived for the generalized…

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…