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.

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.

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.

THREE-POINT CORRELATION FUNCTIONS OF THE MINIMAL CONFORMAL THEORIES COUPLED TO 2D GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3601-3612 ◽  
Author(s):  
Vl. S. DOTSENKO
Keyword(s):  
Operator Algebra ◽  
Correlation Functions ◽  
2D Gravity ◽  
Coulomb Gas ◽  
Field Theories ◽  
Algebra Structure ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Point Correlation ◽  
Structure Constants

The general three-point correlation functions of the minimal conformal field theories coupled to gravity are calculated using the specific Coulomb gas type quantization technique. The gravity interaction modifies in an essential way the operator algebra of the corresponding minimal model, in particular in canceling the decoupling of a finite number of primary fields, in case of rational theories. This is suggested to be related to the appearance of new physical states, under the BRST analysis of Lian and Zuckerman. Within the analytic technique, this effect is due to the corresponding singularities of the gravity sector operator algebra structure constants.

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.

scholarly journals Instability of complex CFTs with operators in the principal series

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Dario Benedetti
Keyword(s):  
Principal Series ◽  
Conformal Group ◽  
Point Of View ◽  
Field Theories ◽  
Operator Product ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Primary Operator ◽  
Tensor Models

Abstract We prove the instability of d-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension h = $$ \frac{d}{2} $$ d 2 + i r, with non-vanishing r ∈ ℝ. From an AdS/CFT point of view, this corresponds to a well-known tachyonic instability, associated to a violation of the Breitenlohner-Freedman bound in AdSd+1; we derive it here directly for generic d-dimensional CFTs that can be obtained as limits of multiscalar quantum field theories, by applying the harmonic analysis for the Euclidean conformal group to perturbations of the conformal solution in the two-particle irreducible (2PI) effective action. Some explicit examples are discussed, such as melonic tensor models and the biscalar fishnet model.

scholarly journals On 2d CFTs that interpolate between minimal models

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Structure Constants

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

scholarly journals ON DUBROVIN TOPOLOGICAL FIELD THEORIES

1994 ◽  
Vol 09 (08) ◽  
pp. 749-760 ◽  
Author(s):  
J.-B. ZUBER
Keyword(s):  
Topological Field Theories ◽  
Coxeter Groups ◽  
Field Theories ◽  
Operator Product ◽  
Conformal Field Theories ◽  
Topological Algebras ◽  
Dual Algebra ◽  
Conformal Field ◽  
Topological Field ◽  
Product Algebra

I show that the new topological field theories recently associated by Dubrovin with each Coxeter group may all be obtained in a simple way by a "restriction" of the standard ADE solutions. I then study the Chebyshev specializations of these topological algebras, examine how the Coxeter graphs and matrices reappear in the dual algebra and mention the intriguing connection with the operator product algebra of conformal field theories. A direct understanding of the occurrence of Coxeter groups in that context is highly desirable.

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.

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