General Bootstrap Equations in 4D CFTs
Abstract
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.
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).Attached Files
Published - 10.1007_2FJHEP01_2018_130.pdf
Submitted - 1705.05401.pdf
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Additional details
- Eprint ID
- 77561
- Resolver ID
- CaltechAUTHORS:20170518-100126278
- Department of Energy (DOE)
- DE-SC0011632
- SCOAP3
- Created
-
2017-05-18Created from EPrint's datestamp field
- Updated
-
2021-11-15Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2017-023