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.

13 pages, 3 figures

References in corpus (6)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Folding Amplitudes into Form Factors: An Antipodal Duality
• Lifting Heptagon Symbols to Functions
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• A simple collinear limit of scattering amplitudes at strong coupling

Cited by in corpus (4)

• Antipodal Self-Duality for a Four-Particle Form Factor
• Antipodal self-duality of square fishnet graphs
• Generalized symmetries as homotopy Lie algebras
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons