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Weight shifting operators and conformal blocks

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3]
  1. International School for Advanced Studies (SISSA) and Italian National Inst. of Nuclear Physics (INFN), Trfieste (Italy); Calfornia Inst. of Technology, Pasadena (United States)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States). Water Burke Inst. for Theoretical Physics
  3. California Inst. of Technology (CalTech), Pasadena, CA (United States). Water Burke Inst. for Theoretical Physics; Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
+ Show Author Affiliations
We introduce a large class of conformally-covariant differential operators and a crossing equation that they obey. Together, these tools dramatically simplify calculations involving operators with spin in conformal field theories. As an application, we derive a formula for a general conformal block (with arbitrary internal and external representations) in terms of derivatives of blocks for external scalars. In particular, our formula gives new expressions for “seed conformal blocks” in 3d and 4d CFTs. We also find simple derivations of identities between external-scalar blocks with different dimensions and internal spins. We comment on additional applications, including deriving recursion relations for general conformal blocks, reducing inversion formulae for spinning operators to inversion formulae for scalars, and deriving identities between general 6j symbols (Racah-Wigner coefficients/“crossing kernels”) of the conformal group.
Research Organization:
California Inst. of Technology, Pasadena (United States); Inst. for Advanced Study, Princeton, NJ (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Grant/Contract Number:
SC0009988; SC0011632
OSTI ID:
1502431
Alternate ID(s):
OSTI ID: 22739085
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2018; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (34)

More on holographic correlators: twisted and dimensionally reduced structures journal April 2021
Lightcone expansions of conformal blocks in closed form journal June 2020
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications text January 2018
Spinning conformal defects text January 2018
Spinor-Helicity Formalism for Massless Fields in AdS$_4$ II: Potentials text January 2019
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
Recursion relations in Witten diagrams and conformal partial waves journal May 2019
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
Beyond a = c : gravitational couplings to matter and the stress tensor OPE journal July 2018
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory journal July 2018
Exact correlation functions in conformal fishnet theory journal August 2019
Universality at large transverse spin in defect CFT journal September 2018
Scalar CFTs and their large N limits journal September 2018
Veneziano amplitude of Vasiliev theory journal October 2018
Harmonic analysis and mean field theory journal October 2019
Light-ray operators in conformal field theory journal November 2018
Recursion relation for general 3d blocks journal December 2019
An introduction to the SYK model journal July 2019
The conformal bootstrap: Theory, numerical techniques, and applications journal January 2019
From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models text January 2017
From spinning conformal blocks to matrix Calogero-Sutherland models text January 2018
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory text January 2018
Universality at large transverse spin in defect CFT 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 CFTs and Their Large N Limits text January 2017
Scalar-Fermion Analytic Bootstrap in 4D preprint January 2017
Light-ray operators in conformal field theory text January 2018
Recursion Relations in Witten Diagrams and Conformal Partial Waves text January 2018

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