scholarly journals Conformal two-point correlation functions from the operator product expansion

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
Jean-François Fortin ◽  
Valentina Prilepina ◽  
Witold Skiba
Keyword(s):  
Correlation Functions ◽  
Operator Product Expansion ◽  
Operator Product ◽  
Point Correlation

scholarly journals Logarithmic Operators in Conformal Field Theory and the ${\mathcal W}_\infty$-Algebra

1997 ◽  
Vol 12 (21) ◽  
pp. 3723-3738 ◽  
Author(s):  
A. Shafiekhani ◽  
M. R. Rahimi Tabar
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Operator Product Expansion ◽  
Field Theories ◽  
Operator Product ◽  
Tensor Operator ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Point Correlation

It is shown explicitly that the correlation functions of conformal field theories (CFT) with the logarithmic operators are invariant under the differential realization of Borel subalgebra of [Formula: see text]-algebra. This algebra is constructed by tensor-operator algebra of differential representation of ordinary [Formula: see text]. This method allows us to write differential equations which can be used to find general expression for three- and four-point correlation functions possessing logarithmic operators. The operator product expansion (OPE) coefficients of general logarithmic CFT are given up to third level.

scholarly journals Conformal four-point correlation functions from the operator product expansion

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Jean-François Fortin ◽  
Valentina Prilepina ◽  
Witold Skiba
Keyword(s):  
Lorentz Group ◽  
Correlation Functions ◽  
Operator Product Expansion ◽  
Gegenbauer Polynomials ◽  
Operator Product ◽  
Symmetric Tensors ◽  
Conformal Blocks ◽  
Relevant Group ◽  
Point Correlation

Abstract We show how to compute conformal blocks of operators in arbitrary Lorentz representations using the formalism described in [1, 2] and present several explicit examples of blocks derived via this method. The procedure for obtaining the blocks has been reduced to (1) determining the relevant group theoretic structures and (2) applying appropriate predetermined substitution rules. The most transparent expressions for the blocks we find are expressed in terms of specific substitutions on the Gegenbauer polynomials. In our examples, we study operators which transform as scalars, symmetric tensors, two-index antisymmetric tensors, as well as mixed representations of the Lorentz group.

scholarly journals USE OF NILPOTENT WEIGHTS IN LOGARITHMIC CONFORMAL FIELD THEORIES

2003 ◽  
Vol 18 (25) ◽  
pp. 4747-4770 ◽  
Author(s):  
S. MOGHIMI-ARAGHI ◽  
S. ROUHANI ◽  
M. SAADAT
Keyword(s):  
Correlation Functions ◽  
Brst Symmetry ◽  
Momentum Tensor ◽  
Field Theories ◽  
Scale Transformation ◽  
Operator Product ◽  
Conformal Weight ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Point Correlation

We show that logarithmic conformal field theories may be derived using nilpotent scale transformation. Using such nilpotent weights we derive properties of LCFT's, such as two and three point correlation functions solely from symmetry arguments. Singular vectors and the Kac determinant may also be obtained using these nilpotent variables, hence the structure of the four point functions can also be derived. This leads to non homogeneous hypergeometric functions. Also we consider LCFT's near a boundary. Constructing "superfields" using a nilpotent variable, we show that the superfield of conformal weight zero, composed of the identity and the pseudo identity is related to a superfield of conformal dimension two, which comprises of energy momentum tensor and its logarithmic partner. This device also allows us to derive the operator product expansion for logarithmic operators. Finally we discuss the AdS/LCFT correspondence and derive some correlation functions and a BRST symmetry.

CORRELATION FUNCTIONS AND OPE IN TWO-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (25) ◽  
pp. 2271-2279 ◽  
Author(s):  
YOSHIAKI TANII ◽  
SHUN-ICHI YAMAGUCHI
Keyword(s):  
Correlation Functions ◽  
Field Theories ◽  
Operator Product ◽  
Theory Approach ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Dimensional Gravity ◽  
Point Correlation ◽  
Liouville Field Theory ◽  
The Continuum

We compute a class of four-point correlation functions of physical operators on a sphere in the unitary minimal conformal field theories coupled to 2-dimensional gravity. We use the continuum Liouville field theory approach and they are obtained as integrals over the moduli (positions of the operators). We examine the integrands near the boundaries of the moduli space and compare their singular behaviors with the operator product expansion.

scholarly journals LIOUVILLE THEORY AND LOGARITHMIC SOLUTIONS TO KNIZHNIK–ZAMOLODCHIKOV EQUATION

2005 ◽  
Vol 20 (20n21) ◽  
pp. 4821-4862 ◽  
Author(s):  
GASTÓN GIRIBET ◽  
CLAUDIO SIMEONE
Keyword(s):  
Correlation Functions ◽  
Three Dimensional ◽  
Liouville Theory ◽  
Operator Product ◽  
De Sitter ◽  
Conformal Field ◽  
Point Correlation ◽  
Symmetry Transformations ◽  
Logarithmic Singularities ◽  
Zamolodchikov Equation

We study a class of solutions to the SL (2, ℝ)k Knizhnik–Zamolodchikov equation. First, logarithmic solutions which represent four-point correlation functions describing string scattering processes on three-dimensional anti-de Sitter space are discussed. These solutions satisfy the factorization ansatz and include logarithmic dependence on the SL (2, ℝ)-isospin variables. Different types of logarithmic singularities arising are classified and the interpretation of these is discussed. The logarithms found here fit into the usual pattern of the structure of four-point function of other examples of AdS/CFT correspondence. Composite states arising in the intermediate channels can be identified as the phenomena responsible for the appearance of such singularities in the four-point correlation functions. In addition, logarithmic solutions which are related to nonperturbative (finite k) effects are found. By means of the relation existing between four-point functions in Wess–Zumino–Novikov–Witten model formulated on SL (2, ℝ) and certain five-point functions in Liouville quantum conformal field theory, we show how the reflection symmetry of Liouville theory induces particular ℤ2 symmetry transformations on the WZNW correlators. This observation allows to find relations between different logarithmic solutions. This Liouville description also provides a natural explanation for the appearance of the logarithmic singularities in terms of the operator product expansion between degenerate and puncture fields.

scholarly journals OPE for XXX

2018 ◽  
Vol 30 (06) ◽  
pp. 1840006 ◽  
Author(s):  
Philippe Di Francesco ◽  
Fedor Smirnov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Experimental Data ◽  
Correlation Functions ◽  
Spin Chain ◽  
Operator Product Expansion ◽  
The Other ◽  
Operator Product ◽  
Quantum Field ◽  
Xxx Model

We explain a new method for finding the correlation functions for the XXX model which is based on the concepts of Operator Product Expansion of Quantum Field Theory on one hand and of fermionic bases for the XXX spin chain on the other. With this method, we are able to perform computations for up to 11 lattice sites. We show that these “experimental” data allow to guess exact formulae for the OPE coefficients. In memory of Ludwig Dmitrievich Faddeev

scholarly journals THE FREE FIELD REPRESENTATION OF SU(3) CONFORMAL FIELD THEORY

1993 ◽  
Vol 08 (23) ◽  
pp. 4031-4053
Author(s):  
HOVIK D. TOOMASSIAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Free Field ◽  
Field Representation ◽  
Conformal Field ◽  
Point Correlation

The structure of the free field representation and some four-point correlation functions of the SU(3) conformal field theory are considered.

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

Sign in / Sign up

Export Citation Format

Share Document