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.

arXiv comment35 pages; v2: references added/updated, revised version

References in corpus (31)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Relations for Gauge-Theory Amplitudes
• Perturbative Gauge Theory As A String Theory In Twistor Space
• New Recursion Relations for Tree Amplitudes of Gluons
• Scattering of Massless Particles in Arbitrary Dimension
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Minimal Basis for Gauge Theory Amplitudes
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Ambitwistor strings and the scattering equations
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit
• Conformal Supergravity in Twistor-String Theory
• Einstein Gravity from Conformal Gravity
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• The Kinematic Algebras from the Scattering Equations
• On the U(1) duality anomaly and the S-matrix of N=4 supergravity
• Integration Rules for Scattering Equations
• Testing Gluon Self-Interactions in Three Jet Events at Hadron Colliders
• RNS derivation of N-point disk amplitudes from the revisited S-matrix approach
• New Relations for Gauge-Theory Amplitudes with Matter
• Evaluation of the CHY Gauge Amplitude
• New Formulas for Amplitudes from Higher-Dimensional Operators
• Revisiting the S-matrix approach to the open superstring low energy effective lagrangian
• On the solutions of the scattering equations
• Analytic Representations of Yang-Mills Amplitudes
• Graviton and gluon scattering from first principles
• Connecting the ambitwistor and the sectorized heterotic strings
• Looking for Gluon Substructure at the Tevatron
• CHY formula and MHV amplitudes
• Derivation of Feynman Rules for Higher Order Poles Using Cross-ratio Identities in CHY Construction

Cited by in corpus (32)

• Aspects of Scattering Amplitudes and Moduli Space Localization
• Double copy structure of CFT correlators
• Heterotic and bosonic string amplitudes via field theory
• Double Copy from Homotopy Algebras
• Gluons and gravitons at one loop from ambitwistor strings
• Are all supergravity theories Yang-Mills squared?
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Celestial operator products from the worldsheet
• Unraveling conformal gravity amplitudes
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Gauge $\times$ Gauge on Spheres
• Connecting the ambitwistor and the sectorized heterotic strings
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• Field theory actions for ambitwistor string and superstring
• On the New Factorizations of Yang-Mills Amplitudes
• Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet
• Yang-Mills theory from the worldsheet
• Bosonic sectorized strings and the $(DF{)}^2$ theory
• Scattering of conformal higher spin fields
• One-loop diagrams with quadratic propagators from the worldsheet
• Hidden Conformal Invariance of Scalar Effective Field Theories
• Supertwistor description of ambitwistor strings
• Recursion and worldsheet formulae for 6d superamplitudes
• Ambitwistor Strings in Six and Five Dimensions
• New Worldsheet Formulae for Conformal Supergravity Amplitudes
• Bootstrapping solutions of scattering equations
• Analytical amplitudes from numerical solutions of the scattering equations
• 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