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General Bootstrap Equations in 4D CFTs

Cuomo, Gabriel Francisco and Karateev, Denis and Kravchuk, Petr (2018) General Bootstrap Equations in 4D CFTs. Journal of High Energy Physics, 2018 (1). Art. No. 130. ISSN 1126-6708. doi:10.1007/JHEP01(2018)130.

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We provide a framework for generic 4D conformal bootstrap computations. It is based on the unification of two independent approaches, the covariant (embedding) formalism and the non-covariant (conformal frame) formalism. We construct their main ingredients (tensor structures and differential operators) and establish a precise connection between them. We supplement the discussion by additional details like classification of tensor structures of n-point functions, normalization of 2-point functions and seed conformal blocks, Casimir differential operators and treatment of conserved operators and permutation symmetries. Finally, we implement our framework in a Mathematica package and make it freely available.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Cuomo, Gabriel Francisco0000-0003-4668-9010
Karateev, Denis0000-0003-4319-9681
Kravchuk, Petr0000-0003-0977-3686
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: June 30, 2017; Accepted: December 10, 2017; Published: January 25, 2018. We thank Alejandra Castro, Tolya Dymarsky, Emtinan Elkhidir, Gabriele Ferretti, Diego Hofman, Hugh Osborn, João Penedones, Riccardo Rattazzi, Fernando Rejón-Barrera, Slava Rychkov, Volker Schomerus, David Simmons-Duffin, Marco Serone and Alessandro Vichi for useful discussions. We particularly thank Marco Serone for his valuable comments on the draft and Emtinan Elkhidir for collaboration on the initial stages of this work. DK and PK are grateful to the organizers of Boostrap 2016 workshop and the Galileo Galilei Institute for Theoretical Physics where the main ideas of this project were born. PK would like to thank the Institute for Advanced Study, where part of this work was completed, for hospitality. This work is supported in part by the DOE grant DE-SC0011632 (PK).
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Subject Keywords:Conformal Field Theory; Nonperturbative Effects
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Issue or Number:1
Record Number:CaltechAUTHORS:20170518-100126278
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Official Citation:Cuomo, G.F., Karateev, D. & Kravchuk, P. J. High Energ. Phys. (2018) 2018: 130.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77561
Deposited By: Joy Painter
Deposited On:18 May 2017 17:36
Last Modified:15 Nov 2021 17:32

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