Thermal conformal blocks

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.

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

Modern Physics Letters A ◽

10.1142/s0217732321502722 ◽

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”.

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On 2d CFTs that interpolate between minimal models

SciPost Physics ◽

10.21468/scipostphys.6.6.075 ◽

2019 ◽

Vol 6 (6) ◽

Cited By ~ 3

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.

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

Journal of High Energy Physics ◽

10.1007/jhep09(2020)111 ◽

2020 ◽

Vol 2020 (9) ◽

Cited By ~ 1

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.

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BRAIDING MATRICES OF CONFORMAL BLOCKS AND COSET MODELS

International Journal of Modern Physics A ◽

10.1142/s0217751x90000118 ◽

1990 ◽

Vol 05 (01) ◽

pp. 211-222 ◽

Cited By ~ 3

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.

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Contour integral representations for the characters of rational conformal field theories

Nuclear Physics B ◽

10.1016/0550-3213(89)90136-3 ◽

1989 ◽

Vol 326 (2) ◽

pp. 351-375 ◽

Cited By ~ 6

Author(s):

Sunil Mukhi ◽

Sudhakar Panda ◽

Ashoke Sen

Keyword(s):

Integral Representations ◽

Field Theories ◽

Contour Integral ◽

Conformal Field Theories ◽

Conformal Field

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Recursion relations for 5-point conformal blocks

Journal of High Energy Physics ◽

10.1007/jhep10(2021)160 ◽

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.

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Towards Feynman rules for conformal blocks

Journal of High Energy Physics ◽

10.1007/jhep01(2021)005 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Sarah Hoback ◽

Sarthak Parikh

Keyword(s):

Field Theory ◽

Effective Field Theory ◽

Hypergeometric Functions ◽

Power Series Expansion ◽

Effective Field ◽

Conformal Block ◽

Tree Level ◽

Conformal Blocks ◽

Simple Set ◽

Feynman Rules

Abstract We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.

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Defects and perturbation

Journal of High Energy Physics ◽

10.1007/jhep04(2021)300 ◽

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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