Weight shifting operators and conformal blocks

Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David

doi:10.1007/jhep02(2018)081

Title: Weight shifting operators and conformal blocks

Journal Article · Wed Feb 14 00:00:00 EST 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep02(2018)081· OSTI ID:1502431

Karateev, Denis ^[1]; Kravchuk, Petr ^[2]; Simmons-Duffin, David ^[3]

International School for Advanced Studies (SISSA) and Italian National Inst. of Nuclear Physics (INFN), Trfieste (Italy)
California Inst. of Technology (CalTech), Pasadena, CA (United States). Water Burke Inst. for Theoretical Physics
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

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.

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Research Organization:: Institute for Advanced Study, Princeton, NJ (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0009988; SC0011632

OSTI ID:: 1502431

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

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Cited by: 99 works

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Bootstrapping SCFTs with Four Supercharges Bobev, Nikolay; El-Showk, Sheer; Mazac, Dalimil arXiv https://doi.org/10.48550/arxiv.1503.02081	text	January 2015

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Scalar-fermion analytic bootstrap in 4D Elkhidir, Emtinan; Karateev, Denis Journal of High Energy Physics, Vol. 2019, Issue 6 https://doi.org/10.1007/jhep06(2019)026	journal	June 2019
Fermion conformal bootstrap in 4d Karateev, Denis; Kravchuk, Petr; Serone, Marco Journal of High Energy Physics, Vol. 2019, Issue 6 https://doi.org/10.1007/jhep06(2019)088	journal	June 2019
Beyond a = c : gravitational couplings to matter and the stress tensor OPE Meltzer, David; Perlmutter, Eric Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/jhep07(2018)157	journal	July 2018
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory Isachenkov, Mikhail; Schomerus, Volker Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/jhep07(2018)180	journal	July 2018
Exact correlation functions in conformal fishnet theory Gromov, Nikolay; Kazakov, Vladimir; Korchemsky, Gregory Journal of High Energy Physics, Vol. 2019, Issue 8 https://doi.org/10.1007/jhep08(2019)123	journal	August 2019
An introduction to the SYK model Rosenhaus, Vladimir Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 32 https://doi.org/10.1088/1751-8121/ab2ce1	journal	July 2019
Universality at large transverse spin in defect CFT Lemos, Madalena; Liendo, Pedro; Meineri, Marco Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-03901	text	January 2018
Veneziano amplitude of Vasiliev theory Turiaci, Gustavo J.; Zhiboedov, Alexander Journal of High Energy Physics, Vol. 2018, Issue 10 https://doi.org/10.1007/jhep10(2018)034	journal	October 2018
From spinning conformal blocks to matrix Calogero-Sutherland models Schomerus, Volker; Sobko, Evgeny Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-02255	text	January 2018
From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models Schomerus, Volker; Sobko, Evgeny Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-11881	text	January 2017
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory Isachenkov, Mikhail; Schomerus, Volker Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-03900	text	January 2018
Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey Chang, Chi-Ming; Fluder, Martin; Lin, Ying-Hsuan arXiv https://doi.org/10.48550/arxiv.1710.08418	text	January 2017
Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory Isachenkov, Mikhail; Schomerus, Volker arXiv https://doi.org/10.48550/arxiv.1711.06609	text	January 2017
Scalar CFTs and Their Large N Limits Rong, Junchen; Su, Ning arXiv https://doi.org/10.48550/arxiv.1712.00985	text	January 2017
Scalar-Fermion Analytic Bootstrap in 4D Elkhidir, Emtinan; Karateev, Denis arXiv https://doi.org/10.48550/arxiv.1712.01554	preprint	January 2017
Light-ray operators in conformal field theory Kravchuk, Petr; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1805.00098	text	January 2018
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications Poland, David; Rychkov, Slava; Vichi, Alessandro arXiv https://doi.org/10.48550/arxiv.1805.04405	text	January 2018
Recursion Relations in Witten Diagrams and Conformal Partial Waves Zhou, Xinan arXiv https://doi.org/10.48550/arxiv.1812.01006	text	January 2018
More on holographic correlators: twisted and dimensionally reduced structures Behan, Connor; Ferrero, Pietro; Zhou, Xinan Journal of High Energy Physics, Vol. 2021, Issue 4 https://doi.org/10.1007/jhep04(2021)008	journal	April 2021
Lightcone expansions of conformal blocks in closed form Li, Wenliang Journal of High Energy Physics, Vol. 2020, Issue 6 https://doi.org/10.1007/jhep06(2020)105	journal	June 2020
Spinning conformal defects Kobayashi, Nozomu; Nishioka, Tatsuma arXiv https://doi.org/10.48550/arxiv.1805.05967	text	January 2018
Spinor-Helicity Formalism for Massless Fields in AdS$_4$ II: Potentials Nagaraj, Balakrishnan; Ponomarev, Dmitry arXiv https://doi.org/10.48550/arxiv.1912.07494	text	January 2019

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