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The S-matrix bootstrap. Part I: QFT in AdS

Paulos, Miguel F.; Penedones, Joao; Toledo, Jonathan; van Rees, Balt C.; Vieira, Pedro

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Miguel F. Paulos

Joao Penedones

Jonathan Toledo

Balt C. van Rees

Pedro Vieira


We propose a strategy to study massive Quantum Field Theory (QFT) using conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study correlation functions of its boundary operators. We show that these are solutions of the crossing equations in one lower dimension. By sending the curvature radius of the background hyperbolic space to infinity we expect to recover flat-space physics. We explain that this regime corresponds to large scaling dimensions of the boundary operators, and discuss how to obtain the flat-space scattering amplitudes from the corresponding limit of the boundary correlators. We implement this strategy to obtain universal bounds on the strength of cubic couplings in 2D flat-space QFTs using 1D conformal bootstrap techniques. Our numerical results match precisely the analytic bounds obtained in our companion paper using S-matrix bootstrap techniques.


Paulos, M. F., Penedones, J., Toledo, J., van Rees, B. C., & Vieira, P. (2017). The S-matrix bootstrap. Part I: QFT in AdS. Journal of High Energy Physics, 2017(11), Article 133.

Journal Article Type Article
Acceptance Date Nov 7, 2017
Online Publication Date Nov 21, 2017
Publication Date Nov 21, 2017
Deposit Date Feb 1, 2017
Publicly Available Date Dec 13, 2017
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2017
Issue 11
Article Number 133
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Copyright Statement
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.

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