The six-point remainder function to all loop orders in the multi-Regge limit

Understand

We present an all-orders formula for the six-point amplitude of planar maximally supersymmetric N=4 Yang-Mills theory in the leading-logarithmic approximation of multi-Regge kinematics.

• In the MHV helicity configuration, our results agree with an integral formula of Lipatov and Prygarin through at least 14 loops.
• A differential equation linking the MHV and NMHV helicity configurations has a natural action in the space of functions relevant to this problem---the single-valued harmonic polylogarithms introduced by Brown.
• These functions depend on a single complex variable and its conjugate, w and w*, which are quadratically related to the original kinematic variables.