The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes

Understand

We describe the minimal space of polylogarithmic functions that is required to express the six-particle amplitude in planar ${\cal N}=4$ super-Yang-Mills theory through six and seven loops, in the NMHV and MHV sectors respectively.

• This space respects a set of extended Steinmann relations that restrict the iterated discontinuity structure of the amplitude, as well as a cosmic Galois coaction principle that constrains the functions and the transcendental numbers that can appear in the amplitude at special kinematic points.
• To put the amplitude into this space, we must divide it by the BDS-like ansatz and by an additional zeta-valued constant $\rho$.
• For this normalization, we conjecture that the extended Steinmann relations and the coaction principle hold to all orders in the coupling.