The Two-Loop Symbol of all Multi-Regge Regions

TL;DR

This paper analyzes the two-loop n-gluon MHV amplitude symbols in multi-Regge kinematics within N=4 super Yang-Mills theory, revealing a quadratic growth in independent symbols and introducing a new building block for construction.

Contribution

It introduces a novel second building block for constructing symbols of any number of gluons from six- and seven-gluon amplitudes, simplifying the understanding of multi-Regge regions.

Findings

Independent symbols grow quadratically with n

Constructed symbols from two fundamental building blocks

Developed a prototype function matching maximal transcendentality

Abstract

We study the symbol of the two-loop n-gluon MHV amplitude for all Mandelstam regions in multi-Regge kinematics in N=4 super Yang-Mills theory. While the number of distinct Mandelstam regions grows exponentially with n, the increase of independent symbols turns out to be merely quadratic. We uncover how to construct the symbols for any number of external gluons from just two building blocks which are naturally associated with the six- and seven-gluon amplitude, respectively. The second building block is entirely new, and in addition to its symbol, we also construct a prototype function that correctly reproduces all terms of maximal functional transcendentality.