Ambitwistor formulations of $R^2$ gravity and $(DF)^2$ gauge theories

TL;DR

This paper develops ambitwistor string formulations for $R^2$ gravity and $(DF)^2$ gauge theories, extending previous work to higher dimensions and revealing new dualities and representations for gravity amplitudes.

Contribution

It introduces ambitwistor string models for $R^2$ gravity and $(DF)^2$ gauge theories, generalizing conformal gravity to $D$ dimensions and uncovering a novel $(DF)^2$ theory with a photon coupling.

Findings

Formulated $R^2$ gravity and $(DF)^2$ gauge theories as ambitwistor string theories.

Extended conformal gravity ambitwistor models to arbitrary dimensions.

Discovered a new $(DF)^2$ gauge theory with photon coupling to Einstein gravity.

Abstract

We consider $D$-dimensional amplitudes in $R^2$ gravities (conformal gravity in $D=4$) and in the recently introduced $(DF)^2$ gauge theory, from the perspective of the CHY formulae and ambitwistor string theory. These theories are related through the BCJ double-copy construction, and the $(DF)^2$ gauge theory obeys color-kinematics duality. We work out the worldsheet details of these theories and show that they admit a formulation as integrals on the support of the scattering equations, or alternatively, as ambitwistor string theories. For gravity, this generalizes the work done by Berkovits and Witten on conformal gravity to $D$ dimensions. The ambitwistor is also interpreted as a $D$-dimensional generalization of Witten's twistor string (SYM + conformal supergravity). As part of our ambitwistor investigation, we discover another $(DF)^2$ gauge theory containing a photon that couples to Einstein gravity. This theory can provide an alternative KLT description of Einstein gravity compared to the usual Yang-Mills squared.