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

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.

35 pages; v2: references added/updated, revised version

References in corpus (10)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Einstein Gravity from Conformal Gravity
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• New Relations for Gauge-Theory Amplitudes with Matter
• New Formulas for Amplitudes from Higher-Dimensional Operators
• On the solutions of the scattering equations
• Graviton and gluon scattering from first principles
• Connecting the ambitwistor and the sectorized heterotic strings

Cited by in corpus (9)

• Double Copy from Homotopy Algebras
• Celestial operator products from the worldsheet
• Connecting the ambitwistor and the sectorized heterotic strings
• On the New Factorizations of Yang-Mills Amplitudes
• Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet
• One-loop diagrams with quadratic propagators from the worldsheet
• UV consistency conditions for CHY integrands
• On-shell representation and further instances of the 2-split behavior of amplitudes
• Ambitwistor strings and amplitudes in curved backgrounds