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

Understand

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.