Soft Theorems to All Orders from Four-Dimensional Ambitwistor Strings

TL;DR

This paper derives all-order soft theorems for Yang-Mills and gravity amplitudes in four-dimensional ambitwistor string theory, using combinatorics and graph theory to expand amplitudes around the soft limit.

Contribution

It provides a novel derivation of soft theorems to all orders in four-dimensional ambitwistor strings, expanding the understanding of soft limits in gauge and gravity theories.

Findings

Derived soft theorems to arbitrary order for Yang-Mills and gravity.

Applied combinatorics and graph theory to amplitude expansions.

Enhanced the theoretical framework for soft limits in string formalism.

Abstract

We study the behaviour of Yang-Mills and gravity amplitudes under the soft limit in the four-dimensional ambitwistor string formalism and derive their soft theorems to arbitrary order. For this purpose, we apply some mathematics. Methods of combinatorics are used for the expansion of $\delta$ functions, and knowledge of graph theory is used for the expansion of reduced determinants. Based on these preliminaries, we expand the formulas of Yang-Mills and gravity amplitudes about the soft parameter $\epsilon$, and obtain soft theorems to arbitrary order.