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 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.

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 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 FUSION ALGEBRAS INDUCED BY REPRESENTATIONS OF THE MODULAR GROUP

1993 ◽  
Vol 08 (20) ◽  
pp. 3495-3507 ◽  
Author(s):  
W. EHOLZER
Keyword(s):  
Representation Theory ◽  
Modular Group ◽  
Central Charge ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Rational Models ◽  
Conformal Field

Using the representation theory of the subgroups SL 2(ℤp) of the modular group we investigate the induced fusion algebras in some simple examples. Only some of these representations lead to "good" fusion algebras. Furthermore, the conformal dimensions and the central charge of the corresponding rational conformal field theories are calculated. Two series of representations which can be realized by unitary theories are presented. We show that most of the fusion algebras induced by admissible representations are realized in well-known rational models.

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 Holomorphic modular bootstrap revisited

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Justin Kaidi ◽  
Ying-Hsuan Lin ◽  
Julio Parra-Martinez
Keyword(s):  
Differential Equations ◽  
Representation Theory ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

Abstract In this work we revisit the “holomorphic modular bootstrap”, i.e. the classification of rational conformal field theories via an analysis of the modular differential equations satisfied by their characters. By making use of the representation theory of PSL(2, ℤn), we describe a method to classify allowed central charges and weights (c, hi) for theories with any number of characters d. This allows us to avoid various bottlenecks encountered previously in the literature, and leads to a classification of consistent characters up to d = 5 whose modular differential equations are uniquely fixed in terms of (c, hi). In the process, we identify the full set of constraints on the allowed values of the Wronskian index for fixed d ≤ 5.

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 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.

scholarly journals Entanglement and complexity of purification in ( 1+1 )-dimensional free conformal field theories

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Hugo A. Camargo ◽  
Lucas Hackl ◽  
Michal P. Heller ◽  
Alexander Jahn ◽  
Tadashi Takayanagi ◽  
...  
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field
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