Cluster adjacency properties of scattering amplitudes

TL;DR

This paper proposes new analytic relations for planar N=4 super Yang-Mills scattering amplitudes based on cluster algebras, extending Steinmann relations and constraining symbol letters, with detailed analysis of heptagon amplitudes and new multi-loop integrals.

Contribution

It introduces a novel set of relations generalizing Steinmann relations using cluster algebra structures, supported by explicit computations of symbols for complex amplitudes.

Findings

Derived new symbol constraints for scattering amplitudes.

Computed symbols for unknown two- and three-loop integrals.

Supported the conjecture with detailed heptagon amplitude analysis.

Abstract

We conjecture a new set of analytic relations for scattering amplitudes in planar N=4 super Yang-Mills theory. They generalise the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr(4,n). In terms of the symbol, they dictate which letters can appear consecutively. We study heptagon amplitudes and integrals in detail and present symbols for previously unknown integrals at two and three loops which support our conjecture.