The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes

TL;DR

This paper reviews a bootstrap approach for constructing scattering amplitudes in planar N=4 super Yang-Mills theory, leveraging new analytic properties to efficiently determine multi-loop amplitudes for six and seven particles.

Contribution

It introduces the use of extended Steinmann relations and the coaction principle to simplify and determine multi-loop amplitudes in N=4 SYM theory.

Findings

Successfully computed six-particle amplitudes up to six loops.

Determined seven-particle NMHV amplitude symbol to four loops.

Validated the effectiveness of cluster adjacency and coaction in amplitude bootstrap.

Abstract

We review the bootstrap method for constructing six- and seven-particle amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory, by exploiting their analytic structure. We focus on two recently discovered properties which greatly simplify this construction at symbol and function level, respectively: the extended Steinmann relations, or equivalently cluster adjacency, and the coaction principle. We then demonstrate their power in determining the six-particle amplitude through six and seven loops in the NMHV and MHV sectors respectively, as well as the symbol of the NMHV seven-particle amplitude to four loops.