scholarly journals HIGHER EQUATIONS OF MOTION IN LIOUVILLE FIELD THEORY

2004 ◽  
Vol 19 (supp02) ◽  
pp. 510-523 ◽  
Author(s):  
AL. ZAMOLODCHIKOV
Keyword(s):  
Field Theory ◽  
2D Gravity ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Operator Product ◽  
Conformal Field ◽  
Structure Constants ◽  
Positive Integers ◽  
Infinite Set ◽  
Liouville Field Theory

An infinite set of the operator-valued relations in the Liouville field theory is established. These relations are enumerated by a pair of positive integers (m, n), the first (1,1) representative being the usual Liouville equation of motion. The relations are proven in the framework of conformal field theory on a basis of the exact structure constants in the Liouville operator product expansions. Possible applications in 2D gravity are discussed.

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.

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 Higher rank FZZ-dualities

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Thomas Creutzig ◽  
Yasuaki Hikida
Keyword(s):  
Field Theory ◽  
Reduction Method ◽  
Operator Algebras ◽  
The Self ◽  
Liouville Theory ◽  
Conformal Field ◽  
Self Duality ◽  
Higher Rank ◽  
Corner Vertex ◽  
Liouville Field Theory

Abstract We examine strong/weak dualities in two dimensional conformal field theories by generalizing the Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality between Witten’s cigar model described by the $$ \mathfrak{sl}(2)/\mathfrak{u}(1) $$ sl 2 / u 1 coset and sine-Liouville theory. In a previous work, a proof of the FZZ-duality was provided by applying the reduction method from $$ \mathfrak{sl}(2) $$ sl 2 Wess-Zumino-Novikov-Witten model to Liouville field theory and the self-duality of Liouville field theory. In this paper, we work with the coset model of the type $$ \mathfrak{sl}\left(N+1\right)/\left(\mathfrak{sl}(N)\times \mathfrak{u}(1)\right) $$ sl N + 1 / sl N × u 1 and investigate the equivalence to a theory with an $$ \mathfrak{sl}\left(N+\left.1\right|N\right) $$ sl N + 1 N structure. We derive the duality explicitly for N = 2, 3 by applying recent works on the reduction method extended for $$ \mathfrak{sl}(N) $$ sl N and the self-duality of Toda field theory. Our results can be regarded as a conformal field theoretic derivation of the duality of the Gaiotto-Rapčák corner vertex operator algebras Y0,N,N+1[ψ] and YN,0,N+1[ψ−1].

scholarly journals Two point functions in defect CFTs

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Christopher P. Herzog ◽  
Abhay Shrestha
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Physical Space ◽  
Arbitrary Spin ◽  
Momentum Tensor ◽  
Maxwell Theory ◽  
Conformal Field ◽  
Point Correlation

Abstract This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic d-dimensional conformal field theory with a flat p-dimensional defect and d − p = q co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on ℝp× (ℝq/ℤ2) and a free four dimensional Maxwell theory on a wedge.

QUANTUM LIOUVILLE FIELD THEORY ON A MANIFOLD WITH BOUNDARY

1998 ◽  
Vol 13 (25) ◽  
pp. 2057-2063
Author(s):  
S. A. APIKYAN
Keyword(s):  
Field Theory ◽  
Functional Equations ◽  
Ward Identity ◽  
Semiclassical Approximation ◽  
Boundary Structure ◽  
Manifold With Boundary ◽  
Structure Constants ◽  
Liouville Field Theory

This letter studies the quantum Liouville field theory on a manifold with boundary. The boundary conformal Ward identity (CWI) is written and its semiclassical approximation is analyzed. This establishes a method of finding the accessory parameters of the theory with boundary. The boundary structure constants of the theory are defined and the functional equations which determine them are derived.

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 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.

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.

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