The KLT kernel in twistor space

TL;DR

This paper develops a twistor space formulation of the double copy relationship between gauge theory and gravity, providing explicit kernels for tree-level amplitudes and extending to curved spacetimes.

Contribution

It introduces a KLT-like integral kernel in twistor space that explicitly constructs gravity amplitudes from gauge theory data, including new formulas and extensions.

Findings

Explicit double copy kernel in twistor space for gravity amplitudes

Inversion of kernel yields new biadjoint scalar S-matrix formula

Extensions to AdS space and self-dual spacetimes

Abstract

The double copy relationship between Yang-Mills theory and general relativity can be stated in terms of a field theory Kawai-Lewellen-Tye (KLT) momentum kernel, which maps two colour-ordered gluon amplitudes to a graviton amplitude at tree-level. These amplitudes can also be written in compact, helicity-graded representations on twistor space which include the famous Parke-Taylor and Hodges formulae in the maximal helicity violating sector. However, a double copy formulation of these helicity-graded formulae has proved elusive. In this paper, we use graph-theoretic methods to obtain an explicit double copy representation of the tree-level, helicity graded S-matrix of general relativity in terms of a KLT-like integral kernel in twistor space. This integral kernel glues together two colour-ordered integrands for tree-level gluon scattering on twistor space to produce tree-level graviton amplitudes, and admits a chiral splitting into positive and negative helicity degrees of freedom. Furthermore, the kernel can be inverted to obtain a new formula for the tree-level S-matrix of biadjoint scalar theory, which we verify using recursion relations. We also derive extensions of this integral kernel to graviton scattering in anti-de Sitter space and self-dual radiative spacetimes, commenting on their potential double copy interpretations.