Cluster adjacency and the four-loop NMHV heptagon

TL;DR

This paper constructs the four-loop NMHV heptagon amplitude in planar $ ext{N}=4$ super Yang-Mills theory using cluster adjacency, matching known results and providing new predictions in the multi-Regge limit.

Contribution

It introduces a cluster adjacency-based ansatz for the amplitude's symbol and determines its parameters through physical consistency, advancing the understanding of scattering amplitudes at four loops.

Findings

Agreement with previous results up to next-to-leading logarithm in multi-Regge limit

New predictions up to next-to-3-leading-logarithmic accuracy

Construction of the amplitude's symbol using cluster adjacency

Abstract

We exploit the recently described property of cluster adjacency for scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory to construct the symbol of the four-loop NMHV heptagon amplitude. We use a manifestly cluster adjacent ansatz and describe how the parameters of this ansatz are determined using simple physical consistency requirements. We then specialise our answer for the amplitude to the multi-Regge limit, finding agreement with previously available results up to the next-to-leading logarithm, and obtaining new predictions up to (next-to)$^3$-leading-logarithmic accuracy.