Multi-Regge limit of the two-loop five-point amplitudes in N = 4 super Yang-Mills and N = 8 supergravity

• Published in: The journal of high energy physics Vol. 2020; no. 10
• Main Authors: Caron-Huot, Simon, Chicherin, Dmitry, Henn, Johannes, Zhang, Yang, Zoia, Simone
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 28.10.2020; Springer Nature B.V
• Subjects: Amplitudes; Classical and Quantum Gravitation; Elementary Particles; High energy physics; Mathematical analysis; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering; String Theory; Supergravity; Transcendental functions; Yang-Mills theory; Effective Field Theories; Scattering Amplitudes; Supersymmetric Gauge Theory
• ISSN: 1029-8479
• DOI: 10.1007/JHEP10(2020)188

A bstract In previous work, the two-loop five-point amplitudes in N = 4 super Yang-Mills theory and N = 8 supergravity were computed at symbol level. In this paper, we compute the full functional form. The amplitudes are assembled and simplified using the analytic expressions of the two-loop pentagon integrals in the physical scattering region. We provide the explicit functional expressions, and a numerical reference point in the scattering region. We then calculate the multi-Regge limit of both amplitudes. The result is written in terms of an explicit transcendental function basis. For certain non-planar colour structures of the N = 4 super Yang-Mills amplitude, we perform an independent calculation based on the BFKL effective theory. We find perfect agreement. We comment on the analytic properties of the amplitudes.