Antipodal Symmetry of Two-Loop MHV Amplitudes

Abstract

I present a conjecture that all two-loop MHV amplitudes in planar $\mathcal{N}=4$ 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.

arXiv comment13 pages, 3 figures

References in corpus (17)

• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Motivic Amplitudes and Cluster Coordinates
• Thermodynamic Bubble Ansatz
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• How tropical are seven- and eight-particle amplitudes?
• Folding Amplitudes into Form Factors: An Antipodal Duality
• Lifting Heptagon Symbols to Functions
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
• A simple collinear limit of scattering amplitudes at strong coupling

Cited by in corpus (4)

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• Generalized symmetries as homotopy Lie algebras
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons