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Title: Recursion relation for general 3d blocks

Abstract

We derive closed-form expressions for all ingredients of the Zamolodchikov-like recursion relation for general spinning conformal blocks in 3-dimensional conformal field theory. This result opens a path to efficient automatic generation of conformal block tables, which has immediate applications in numerical conformal bootstrap program. Our derivation is based on an understanding of null states and conformally-invariant differential operators in momentum space, combined with a careful choice of the relevant tensor structures bases. This derivation generalizes straightforwardly to higher spacetime dimensions d, provided the relevant Clebsch-Gordan coefficients of Spin (d) are known.

Authors:
 [1];  [2]; ORCiD logo [3]
  1. Yale Univ., New Haven, CT (United States). Dept. of Physics
  2. Princeton Univ., NJ (United States). Joseph Henry Lab. of Physics
  3. Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); Simons Foundation
Contributing Org.:
Perimeter Institute for Theoretical Physics
OSTI Identifier:
1596664
Grant/Contract Number:  
SC0009988; PHY-1820651
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 12; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal and W Symmetry; Conformal Field Theory

Citation Formats

Erramilli, Rajeev S., Iliesiu, Luca V., and Kravchuk, Petr. Recursion relation for general 3d blocks. United States: N. p., 2019. Web. doi:10.1007/JHEP12(2019)116.
Erramilli, Rajeev S., Iliesiu, Luca V., & Kravchuk, Petr. Recursion relation for general 3d blocks. United States. https://doi.org/10.1007/JHEP12(2019)116
Erramilli, Rajeev S., Iliesiu, Luca V., and Kravchuk, Petr. Mon . "Recursion relation for general 3d blocks". United States. https://doi.org/10.1007/JHEP12(2019)116. https://www.osti.gov/servlets/purl/1596664.
@article{osti_1596664,
title = {Recursion relation for general 3d blocks},
author = {Erramilli, Rajeev S. and Iliesiu, Luca V. and Kravchuk, Petr},
abstractNote = {We derive closed-form expressions for all ingredients of the Zamolodchikov-like recursion relation for general spinning conformal blocks in 3-dimensional conformal field theory. This result opens a path to efficient automatic generation of conformal block tables, which has immediate applications in numerical conformal bootstrap program. Our derivation is based on an understanding of null states and conformally-invariant differential operators in momentum space, combined with a careful choice of the relevant tensor structures bases. This derivation generalizes straightforwardly to higher spacetime dimensions d, provided the relevant Clebsch-Gordan coefficients of Spin (d) are known.},
doi = {10.1007/JHEP12(2019)116},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2019,
place = {United States},
year = {2019},
month = {12}
}

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