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Title: Casimir recursion relations for general conformal blocks

Journal Article · · Journal of High Energy Physics (Online)
 [1]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
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We study the structure of series expansions of general spinning conformal blocks. We find that the terms in these expansions are naturally expressed by means of special functions related to matrix elements of Spin(d) representations in Gelfand-Tsetlin basis, of which the Gegenbauer polynomials are a special case. We study the properties of these functions and explain how they can be computed in practice. We show how the Casimir equation in Dolan-Osborn coordinates leads to a simple one-step recursion relation for the coefficients of the series expansion of general spinning conformal block. The form of this recursion relation is determined by 6j symbols of Spin(d – 1). In particular, it can be written down in closed form in d = 3, d = 4, for seed blocks in general dimensions, or in any other situation when the required 6j symbols can be computed. As a result, we work out several explicit examples and briefly discuss how our recursion relation can be used for efficient numerical computation of general conformal blocks.

Research Organization:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
SC0011632
OSTI ID:
1499658
Journal Information:
Journal of High Energy Physics (Online), Vol. 2018, Issue 2; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 36 works
Citation information provided by
Web of Science

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Cited By (22)

Multipoint conformal blocks in the comb channel journal February 2019
Mellin amplitudes for fermionic conformal correlators journal March 2018
Spheres, charges, instantons, and bootstrap: A five-dimensional odyssey journal March 2018
From spinning conformal blocks to matrix Calogero-Sutherland models journal April 2018
Scalar-fermion analytic bootstrap in 4D journal June 2019
Fermion conformal bootstrap in 4d journal June 2019
A spacetime derivation of the Lorentzian OPE inversion formula journal July 2018
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory journal July 2018
Veneziano amplitude of Vasiliev theory journal October 2018
The conformal bootstrap at finite temperature journal October 2018
Harmonic analysis and mean field theory journal October 2019
Recursion relation for general 3d blocks journal December 2019
The conformal bootstrap: Theory, numerical techniques, and applications journal January 2019
Canonical relativistic formulation to calculate the Casimir force four-vector on anisotropic conductor polarizable and magnetizable media journal September 2019
From spinning conformal blocks to matrix Calogero-Sutherland models text January 2018
From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models text January 2017
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory text January 2018
Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey text January 2017
Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory text January 2017
Scalar-Fermion Analytic Bootstrap in 4D preprint January 2017
The Conformal Bootstrap at Finite Temperature text January 2018
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications text January 2018

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