scholarly journals Recursion relations for 5-point conformal blocks

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
David Poland ◽  
Valentina Prilepina
Keyword(s):  
Linear Combination ◽  
Energy Operator ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Point Function ◽  
Conformal Blocks ◽  
Recursion Relations ◽  
Expectation Value ◽  
Conformal Field ◽  
Weight Shifting

Abstract We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars.

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 Scalar Dyon Production In Near Extremal Kerr-Newman Black Holes

2018 ◽  
Vol 168 ◽  
pp. 01011
Author(s):  
Chiang-Mei Chen ◽  
Sang Pyo Kim ◽  
Jia-Rui Sun ◽  
Fu-Yi Tang
Keyword(s):  
Black Holes ◽  
Pair Production ◽  
Cross Section ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Cross Section Ratio ◽  
Point Function ◽  
Charged Scalar ◽  
Conformal Field ◽  
Horizon Geometry

The pair production of charged scalar dyons is analytically studied in near-extremal Kerr-Newman (KN) dyonic black holes. The pair production rate and its thermal interpretation are given. Moreover, the absorption cross section ratio has been compared with the two-point function of the conformal field theories (CFTs) holographically dual to the near horizon geometry, namely warped AdS3, of the near extremal Kerr-Newman black holes to verify the threefold dyonic KN/CFTs correspondence.

scholarly journals Momentum space parity-odd CFT 3-point functions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sachin Jain ◽  
Renjan Rajan John ◽  
Abhishek Mehta ◽  
Amin A. Nizami ◽  
Adithya Suresh
Keyword(s):  
Momentum Space ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Ward Identities ◽  
Conformal Field ◽  
Weight Shifting ◽  
Conserved Currents

Abstract We study the parity-odd sector of 3-point functions comprising scalar operators and conserved currents in conformal field theories in momentum space. We use momentum space conformal Ward identities as well as spin-raising and weight-shifting operators to fix the form of some of these correlators. Wherever divergences appear we discuss their regularisation and renormalisation using appropriate counter-terms.

scholarly journals Pole-skipping of scalar and vector fields in hyperbolic space: conformal blocks and holography

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Yongjun Ahn ◽  
Viktor Jahnke ◽  
Hyun-Sik Jeong ◽  
Keun-Young Kim ◽  
Kyung-Sun Lee ◽  
...  
Keyword(s):  
Hyperbolic Space ◽  
Vector Fields ◽  
Field Theories ◽  
Late Time ◽  
Time Behavior ◽  
Conformal Field Theories ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Scalar And Vector Fields ◽  
Pole Structure

Abstract Motivated by the recent connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators (OTOCs), we study the pole structure of thermal two-point functions in d-dimensional conformal field theories (CFTs) in hyperbolic space. We derive the pole-skipping points of two-point functions of scalar and vector fields by three methods (one field theoretic and two holographic methods) and confirm that they agree. We show that the leading pole-skipping point of two point functions is related with the late time behavior of conformal blocks and shadow conformal blocks in four-point OTOCs.

BRAIDING MATRICES OF CONFORMAL BLOCKS AND COSET MODELS

1990 ◽  
Vol 05 (01) ◽  
pp. 211-222 ◽  
Author(s):  
H. ITOYAMA ◽  
A. SEVRIN
Keyword(s):  
Ising Model ◽  
Spectral Parameter ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Blocks ◽  
Toda System ◽  
Conformal Field ◽  
Coset Models ◽  
Zamolodchikov Equation ◽  
Current Algebras

We explain, from the Knizhnik-Zamolodchikov equation, the coincidence of the braiding matrices of conformal field theories having current algebras with face Boltzmann weights (at infinite spectral parameter) of the corresponding generalized Toda system (GTS). A vertex-height correspondence is introduced in the WZW theory. Braiding matrices of coset models are found to factorize into those of the WZW theories and, as an example, we evaluate those of the Ising model.

scholarly journals A nilpotency index of conformal manifolds

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Zohar Komargodski ◽  
Shlomo S. Razamat ◽  
Orr Sela ◽  
Adar Sharon
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Generic Point ◽  
Expectation Value ◽  
Conformal Field ◽  
Chiral Ring ◽  
Nilpotency Index ◽  
Conformal Manifolds

Abstract We show that exactly marginal operators of Supersymmetric Conformal Field Theories (SCFTs) with four supercharges cannot obtain a vacuum expectation value at a generic point on the conformal manifold. Exactly marginal operators are therefore nilpotent in the chiral ring. This allows us to associate an integer to the conformal manifold, which we call the nilpotency index of the conformal manifold. We discuss several examples in diverse dimensions where we demonstrate these facts and compute the nilpotency index.

scholarly journals Thermal conformal blocks

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
Yan Gobeil ◽  
Alexander Maloney ◽  
Gim Seng Ng ◽  
Jie-qiang Wu
Keyword(s):  
Hypergeometric Functions ◽  
Analytic Formula ◽  
Conformal Block ◽  
Integral Representations ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Blocks ◽  
Generalized Hypergeometric Functions ◽  
Conformal Field ◽  
General Dimension

We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second-order Casimir differential equations and have integral representations related to AdS Witten diagrams. We give an analytic formula for the scalar conformal block in terms of generalized hypergeometric functions. As an application, we deduce an asymptotic formula for the three-point coefficients of primary operators in the limit where two of the operators are heavy.

scholarly journals PURELY AFFINE ELEMENTARY su(N) FUSIONS

2002 ◽  
Vol 17 (19) ◽  
pp. 1249-1258 ◽  
Author(s):  
JØRGEN RASMUSSEN ◽  
MARK A. WALTON
Keyword(s):  
Linear Combination ◽  
Lie Algebras ◽  
Tensor Products ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Simple Lie Algebras ◽  
Conformal Field ◽  
Highest Weight ◽  
Highest Weight Representations

We consider three-point couplings in simple Lie algebras — singlets in triple tensor products of their integrable highest weight representations. A coupling can be expressed as a linear combination of products of finitely many elementary couplings. This carries over to affine fusion, the fusion of Wess–Zumino–Witten conformal field theories, where the expressions are in terms of elementary fusions. In the case of su(4) it has been observed that there is a purely affine elementary fusion, i.e. an elementary fusion that is not an elementary coupling. In this paper we show by construction that there is at least one purely affine elementary fusion associated to every su (N > 3).

scholarly journals Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block

2021 ◽  
Vol 36 (39) ◽  
Author(s):  
Yu Nakayama
Keyword(s):  
Representation Theory ◽  
Hypergeometric Function ◽  
Conformal Block ◽  
Field Theories ◽  
Gauss Hypergeometric Function ◽  
Conformal Field Theories ◽  
Recursive Structure ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Pole Structure

The Gauß hypergeometric function shows a recursive structure which resembles those found in conformal blocks. We compare it with the recursive structure of the conformal block in boundary/crosscap conformal field theories that is obtained from the representation theory. We find that the pole structure perfectly agrees but the recursive structure in the Gauß hypergeometric function is slightly “off-shell”.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

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