Multi-Regge limit of the two-loop five-point amplitudes in N $$ \mathcal{N} $$ = 4 super Yang-Mills and N
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Springer
Received: March Revised: September Accepted: September Published: October
23, 22, 23, 28,
2020 2020 2020 2020
Simon Caron-Huot,a Dmitry Chicherin,b Johannes Henn,b Yang Zhangc,d and Simone Zoiab a
Department of Physics, McGill University, 3600 Rue University, Montr´eal, QC Canada b Max-Planck-Institut f¨ ur Physik, Werner-Heisenberg-Institut, D-80805 M¨ unchen, Germany c Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, China d Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei, Anhui 230026, China
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: In previous work, the two-loop five-point amplitudes in N = 4 super YangMills 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. Keywords: Scattering Amplitudes, Effective Field Theories, Supersymmetric Gauge Theory ArXiv ePrint: 2003.03120
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)188
JHEP10(2020)188
Multi-Regge limit of the two-loop five-point amplitudes in N = 4 super Yang-Mills and N = 8 supergravity
Contents 1 Introduction
1
2 Kinematics and pentagon functions
3
3.6
two-loop five-point N = 4 sYM and N = 8 supergravity amplitudes 5 Expected structure of the two-loop amplitudes 7 Two-loop integrands 9 Pure integral bases 10 Permutation of the external legs and integrated expressions 12 Infrared factorisation and hard functions 12 3.5.1 N = 4 super Yang-Mills 13 3.5.2 N = 8 supergravity 14 The two-loop hard functions 15
4 Multi-Regge limit and pentagon functions 4.1 Multi-Regge kinematics 4.2 Multi-Regge limit of the pure integrals 4.3 Feynman integrals with non-trivial analytic properties 4.4 Transcendental functions for the N = 4 super Yang-Mills amplitude in the multi-Regge limit 4.5 Transcendental functions for the N = 8 supergravity amplitude in the multiRegge limit 5 The 5.1 5.2 5.3
multi-Regge limit of the N = 4 super Yang-Mills amplitude Colour flow in the multi-Regge limit One-loop hard function Two-loop hard function
17 17 19 23 26 29 33 34 36 37
6 Predictions of BFKL theory in N = 4 super Yang-Mills 6.1 General considerations 6.2 Bare amplitude with maximal reggeon exchanges 6.3 Infrared-factorized amplitude 6.4 Examples of non real-analytic amplitudes
39 39 41 42 45
7 The
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