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Weight Shifting Operators and Conformal Blocks

Karateev, Denis and Kravchuk, Petr and Simmons-Duffin, David (2018) Weight Shifting Operators and Conformal Blocks. Journal of High Energy Physics, 2018 (2). Art. No. 81. ISSN 1126-6708. doi:10.1007/JHEP02(2018)081.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Karateev, Denis0000-0003-4319-9681
Kravchuk, Petr0000-0003-0977-3686
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© 2018 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: December 6, 2017; Accepted: January 22, 2018; Published: February 14, 2018. We are grateful to Clay Córdova, Tolya Dymarsky, Abhijit Gadde, Mikhail Isachenkov, Eric Perlmutter, Fernando Rejon-Barrera, Douglas Stanford and Emilio Trevisani for discussions. DK and PK would like to thank the organizers of the Bootstrap 2017 workshop, where part of this work was completed. DSD is supported by DOE grant DE-SC0009988, a William D. Loughlin Membership at the Institute for Advanced Study, and Simons Foundation grant 488657 (Simons Collaboration on the Nonperturbative Bootstrap). PK is supported DOE grant DE-SC0011632.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0009988
Institute for Advanced StudyUNSPECIFIED
Simons Foundation488657
Department of Energy (DOE)DE-SC0011632
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Other Numbering System NameOther Numbering System ID
Issue or Number:2
Record Number:CaltechAUTHORS:20170630-094253636
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Official Citation:Karateev, D., Kravchuk, P. & Simmons-Duffin, D. J. High Energ. Phys. (2018) 2018: 81.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78718
Deposited By: Joy Painter
Deposited On:30 Jun 2017 17:05
Last Modified:15 Nov 2021 17:42

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