Soft Theorems from Conformal Field Theory

TL;DR

This paper uses ambitwistor string theory to derive and analyze soft theorems for gauge and gravity amplitudes, revealing their algebraic structure, connections to color-kinematics duality, and 1-loop corrections.

Contribution

It provides a string-theoretic derivation of soft theorems in 4d Yang-Mills and gravity, including loop corrections and algebraic insights.

Findings

Derived soft theorems as series in soft momentum for gauge and gravity

Connected soft limit algebra to braiding of vertex operators

Computed 1-loop corrections to soft graviton theorem

Abstract

Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambitwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.