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The inversion formula and 6j symbol for 3d fermions

Albayrak, Soner and Meltzer, David and Poland, David (2020) The inversion formula and 6j symbol for 3d fermions. Journal of High Energy Physics, 2020 (9). Art. No. 148. ISSN 1029-8479. doi:10.1007/jhep09(2020)148.

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In this work we study the 6j symbol of the 3d conformal group for fermionic operators. In particular, we study 4-point functions containing two fermions and two scalars and also those with four fermions. By using weight-shifting operators and harmonic analysis for the Euclidean conformal group, we relate these spinning 6j symbols to the simpler 6j symbol for four scalar operators. As one application we use these techniques to compute 3d mean field theory (MFT) OPE coefficients for fermionic operators. We then compute corrections to the MFT spectrum and couplings due to the inversion of a single operator, such as the stress tensor or a low-dimension scalar. These results are valid at finite spin and extend the perturbative large spin analysis to include non-perturbative effects in spin.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Albayrak, Soner0000-0002-9223-0115
Poland, David0000-0003-3854-2430
Additional Information:© 2020 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. Received: June 26, 2020. Accepted: August 6, 2020. Published: September 23, 2020. Article funded by SCOAP3. We thank Petr Kravchuk, Eric Perlmutter, Valentina Prilepina, and David Simmons-Duffin for relevant discussions. SA also thank Petr Kravchuk and David Simmons-Duffin for sharing their previous work on computations with weight shifting operators. The research of DP and SA is supported by DOE grant no. DE-SC0020318 and Simons Foundation grant 488651 (Simons Collaboration on the Nonperturbative Bootstrap). DP and SA also thank the Walter Burke Institute for Theoretical Physics at Caltech for its support and hospitality during the completion of this work. The research of DM is supported by the Walter Burke Institute for Theoretical Physics at Caltech and the Sherman Fairchild Foundation. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0020318
Simons Foundation488651
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Subject Keywords:Conformal and W Symmetry, Conformal Field Theory, Nonperturbative Effects
Issue or Number:9
Record Number:CaltechAUTHORS:20200925-104734754
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Official Citation:Albayrak, S., Meltzer, D. & Poland, D. The inversion formula and 6j symbol for 3d fermions. J. High Energ. Phys. 2020, 148 (2020).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105554
Deposited By: George Porter
Deposited On:25 Sep 2020 19:41
Last Modified:16 Nov 2021 18:44

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