Heptagon functions and seven-gluon amplitudes in multi-Regge kinematics

• Published in: The journal of high energy physics Vol. 2021; no. 12; pp. 1 - 33
• Main Authors: Dixon, Lance J., Liu, Yu-Ting, Miczajka, Julian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2021; Springer Nature B.V; Springer Nature; SpringerOpen
• Subjects: 1/N Expansion; Amplitudes; Classical and Quantum Gravitation; Duality in Gauge Field Theories; Elementary Particles; Gluons; High energy physics; Kinematics; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering Amplitudes; Series expansion; String Theory; Yang-Mills theory; 1; Duality in Gauge Field Theories; Scattering Amplitudes; Expansion
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP12(2021)218

A bstract We compute all 2 → 5 gluon scattering amplitudes in planar N = 4 super-Yang-Mills theory in the multi-Regge limit that is sensitive to the non-trivial (“long”) Regge cut. We provide the amplitudes through four loops and to all logarithmic accuracy at leading power, in terms of single-valued multiple polylogarithms of two variables. To obtain these results, we leverage the function-level results for the amplitudes in the Steinmann cluster bootstrap. To high powers in the series expansion in the two variables, our results agree with the recently conjectured all-order central emission vertex used in the Fourier-Mellin representation of amplitudes in multi-Regge kinematics. Our results therefore provide a resummation of the Fourier-Mellin residues into single-valued polylogarithms, and constitute an important cross-check between the bootstrap approach and the all-orders multi-Regge proposal.