scholarly journals Operator product expansion convergence in conformal field theory

2012 ◽  
Vol 86 (10) ◽  
Author(s):  
Duccio Pappadopulo ◽  
Slava Rychkov ◽  
Johnny Espin ◽  
Riccardo Rattazzi
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Operator Product Expansion ◽  
Operator Product ◽  
Conformal Field

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 Regge theory at finite boost

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Simon Caron-Huot ◽  
Joshua Sandor
Keyword(s):  
Field Theory ◽  
Operator Product Expansion ◽  
Operator Product ◽  
Exact Results ◽  
Double Integral ◽  
Regge Theory ◽  
Conformal Field ◽  
Regge Trajectories ◽  
Continuous Spins ◽  
Regge Limit

Abstract The Operator Product Expansion is a useful tool to represent correlation functions. In this note we extend Conformal Regge theory to provide an exact OPE representation of Lorenzian four-point correlators in conformal field theory, valid even away from Regge limit. The representation extends convergence of the OPE by rewriting it as a double integral over continuous spins and dimensions, and features a novel “Regge block”. We test the formula in the conformal fishnet theory, where exact results involving nontrivial Regge trajectories are available.

scholarly journals OPERATOR PRODUCT EXPANSION IN SL(2) CONFORMAL FIELD THEORY

2002 ◽  
Vol 17 (11) ◽  
pp. 683-693 ◽  
Author(s):  
KAZUO HOSOMICHI ◽  
YUJI SATOH
Keyword(s):  
Field Theory ◽  
Operator Product Expansion ◽  
Field Theories ◽  
Operator Product ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Highest Weight ◽  
Wznw Model ◽  
Highest Weight Representations ◽  
Highest Weight Representation

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 SL(2) weights, and calculate their two- and three-point functions. Using these correlators, we show that the correct OPE is obtained when one of the primary fields belongs to the degenerate highest weight representation. We briefly comment on the OPE in the SL (2,R) WZNW model.

OPERATOR ALGEBRA IN TWO-DIMENSIONAL CONFORMAL FIELD THEORY CONTAINING SPIN 4/3 “PARAFERMIONIC” CONSERVED CURRENTS

1991 ◽  
Vol 06 (11) ◽  
pp. 2005-2023 ◽  
Author(s):  
R.H. POGHOSSIAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Operator Algebra ◽  
Closed Operator ◽  
Operator Product ◽  
Two Dimensional ◽  
Conformal Field ◽  
Structure Constants ◽  
Conserved Currents

Recently Zamolodchikov and Fateev have constructed a series of models of the two-dimensional conformal field theory containing spin 4/3 nonlocal (parafermion) currents. From degenerated fields one can construct a closed operator algebra with respect to the operator product expansions. All the structure constants of this algebra are computed in this paper.

A MATHEMATICA™ PACKAGE FOR COMPUTING OPERATOR PRODUCT EXPANSIONS

1991 ◽  
Vol 02 (03) ◽  
pp. 787-798 ◽  
Author(s):  
K. THIELEMANS
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Free Field ◽  
Standard Form ◽  
General Purpose ◽  
Operator Product ◽  
Conformal Anomaly ◽  
Moody Algebra ◽  
Conformal Field ◽  
Free Field Realization

A general purpose Mathematica™ package for computing Operator Product Expansions of composite operators in meromorphic conformal field theory is described. Given the OPEs for a set of “basic” fields, OPEs of arbitrarily complicated composites can be computed automatically. Normal ordered products are always reduced to a standard form. Two explicit examples are presented: the conformal anomaly for superstrings and a free field realization for the [Formula: see text] Kač-Moody-algebra.

scholarly journals Regge OPE blocks and light-ray operators

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Nozomu Kobayashi ◽  
Tatsuma Nishioka ◽  
Yoshitaka Okuyama
Keyword(s):  
Field Theory ◽  
Operator Product Expansion ◽  
Asymptotic Form ◽  
Vacuum State ◽  
Operator Product ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Regge Behavior ◽  
New Form ◽  
Regge Limit

Abstract 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 state. We demonstrate that the OPE block is dominated by a light-ray operator in the Regge limit, which reproduces precisely the Regge behavior of conformal blocks when used inside scalar four-point functions. Motivated by this observation, we propose a new form of the OPE block, called the light-ray channel OPE block that has a well-behaved expansion dominated by a light-ray operator in the Regge limit. We also show that the two OPE blocks have the same asymptotic form in the Regge limit and confirm the assertion that the Regge limit of a pair of spacelike-separated operators in a Minkowski patch is equivalent to the OPE limit of a pair of timelike-separated operators associated with the original pair in a different Minkowski patch.

INFINITE DIMENSIONAL LIE ALGEBRAS IN 4D CONFORMAL FIELD THEORY

2008 ◽  
Vol 05 (08) ◽  
pp. 1361-1371
Author(s):  
IVAN TODOROV
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Recent Work ◽  
Lie Algebras ◽  
Scalar Fields ◽  
Operator Product ◽  
Positive Energy ◽  
Infinite Dimensional ◽  
Conformal Field ◽  
Compact Gauge Group

It is known that there are no scalar Lie fields in more than two space-time dimensions [4]. Bilocal fields, however, which naturally arise in conformal operator product expansions, do generate infinite Lie algebras. Recent work, [2, 3], is reviewed, in which we classify such algebras and their unitary positive energy representations in a theory of a system of scalar fields of dimension two. The results are linked to the Doplicher–Haag–Roberts theory of superselection sectors governed by a (global) compact gauge group.

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