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The SAGEX review on scattering amplitudes Chapter 5: Analytic bootstraps for scattering amplitudes and beyond

Papathanasiou, G. ORCID: 0000-0002-2627-9906 (2022). The SAGEX review on scattering amplitudes Chapter 5: Analytic bootstraps for scattering amplitudes and beyond. Journal of Physics A: Mathematical and Theoretical, 55(44), article number 443006. doi: 10.1088/1751-8121/ac7e8e


One of the main challenges in obtaining predictions for collider experiments from perturbative quantum field theory, is the direct evaluation of the Feynman integrals it gives rise to. In this chapter, we review an alternative bootstrap method that instead efficiently constructs physical quantities by exploiting their analytic structure. We present in detail the setting where this method has been originally developed, six- and seven-particle amplitudes in the large-color limit of N = 4 super Yang–Mills theory. We discuss the class of functions these amplitudes belong to, and the strong clues mathematical objects known as cluster algebras provide for rendering this function space both finite and of relatively small dimension at each loop order. We then describe how to construct this function space, as well as how to locate the amplitude inside of it with the help of kinematic limits, and apply the general procedure to a concrete example: the determination of the two-loop correction to the first nontrivial six-particle amplitude. We also provide an overview of other areas where the realm of the bootstrap paradigm is expanding, including other scattering amplitudes, form factors and Feynman integrals, and point out the analytic properties of potentially wider applicability that it has revealed.

Publication Type: Article
Additional Information: Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Publisher Keywords: scattering amplitudes, gauge theory, cluster algebras
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology
School of Science & Technology > Mathematics
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