### Speaker

Martin Sprenger
(ETH Zürich)

### Description

In this talk, I will describe the connection between the high-energy limit of the six-gluon scattering amplitude in N=4 super Yang-Mills theory and a certain class of single-valued polylogarithmic functions.
While the evaluation of the six-gluon amplitude to high loop orders in general kinematics is a very difficult problem, the amplitude in the multi-Regge regime is governed by a dispersion-like integral which is fully known even at finite coupling.
However, this dispersion-like integral is formulated in Fourier-Mellin space. Obtaining expressions in momentum space thus requires carrying out said integral which is tedious beyond the lowest loop orders.
I will show how an understanding of the mathematical structure of the single-valued polylogs to which the integral evaluates gives rise to an efficient and algorithmic evaluation of the amplitude and briefly mention extensions to higher-point amplitudes.

### Primary author

Martin Sprenger
(ETH Zürich)