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The S-matrix bootstrap. Part III: higher dimensional amplitudes

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 consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 3+1 dimensions due to crossing symmetry, analyticity and unitarity. We extremize cubic couplings, quartic couplings and scattering lengths relevant for the elastic scattering amplitude of two identical scalar particles. In the cases where our results can be compared with the older S-matrix literature they are in excellent agreement. We also extremize a cubic coupling in 2+1 dimensions which we can directly compare to a universal bound for a QFT in AdS. This paper generalizes our previous 1+1 dimensional results of [1] and [2].


Paulos, M. F., Penedones, J., Toledo, J., van Rees, B. C., & Vieira, P. (2019). The S-matrix bootstrap. Part III: higher dimensional amplitudes. Journal of High Energy Physics, 2019(12), Article 40.

Journal Article Type Article
Acceptance Date Nov 6, 2019
Online Publication Date Dec 4, 2019
Publication Date Dec 31, 2019
Deposit Date Dec 10, 2019
Publicly Available Date Dec 10, 2019
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2019
Issue 12
Article Number 40


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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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