Generating All Tree Amplitudes in N=4 SYM by Inverse Soft Limit

TL;DR

This paper introduces a recursive method using the Inverse Soft Limit to generate all tree-level superamplitudes in N=4 super Yang-Mills theory, revealing their symmetry and soft limit properties.

Contribution

It presents a systematic recursive approach to construct all tree-level superamplitudes in N=4 SYM using Inverse Soft Limit, highlighting manifest Yangian symmetry.

Findings

Amplitudes generated have manifest Yangian symmetry.

The method makes the soft limit behavior transparent.

The approach can be extended to form factors.

Abstract

The idea of adding particles to construct amplitudes has been utilized in various ways in exploring the structure of scattering amplitudes. This idea is often called Inverse Soft Limit, namely it is the reverse mechanism of taking particles to be soft. We apply the Inverse Soft Limit to the tree-level amplitudes in $\mathcal{N}=4$ super Yang-Mills theory, which allows us to generate full tree-level superamplitudes by adding "soft" particles in a certain way. With the help from Britto-Cachazo-Feng-Witten recursion relations, a systematic and concrete way of adding particles is determined recursively. The amplitudes constructed solely by adding particles not only have manifest Yangian symmetry, but also make the soft limit transparent. The method of generating amplitudes by Inverse Soft Limit can also be generalized for constructing form factors.