Antipodal symmetry of two-loop MHV amplitudes

• Published in: The journal of high energy physics Vol. 2022; no. 9; pp. 131 - 13
• Main Author: Liu, Yu-Ting
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 16.09.2022; Springer Nature B.V; SpringerOpen
• Subjects: 1/N Expansion; Algebra; Amplitudes; Antipodes; Classical and Quantum Gravitation; Discrete Symmetries; Elementary Particles; High energy physics; Isomorphism; Kinematics; Parity; Physics; Physics and Astronomy; Polytopes; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering Amplitudes; String Theory; Symmetry; Yang-Mills theory; Discrete Symmetries; 1; Scattering Amplitudes; Expansion
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2022)131

A bstract I present a conjecture that all two-loop MHV amplitudes in planar N = 4 super-Yang-Mills theory possess an antipodal symmetry when evaluated on parity-even kinematics. The symmetry acts as a change of basis on the symbol letters, followed by the antipode operation associated with the Hopf algebra structure of multiple polylogarithms. At the symbol level, I provide the symmetry map explicitly for amplitudes with up to eight external particles, and also provide evidence at all multiplicities. Intriguingly, the map acts as an isomorphism on the normal fans of the Newton polytopes of the symbol letters. The conjectured symmetry is one of the rare known cases where the antipode map shows up in physically important examples.