Conformal Gravity from Gauge Theory

Abstract

We use the duality between color and kinematics to obtain scattering amplitudes in non-minimal conformal N=0,1,2,4 (super)gravity theories. Generic tree amplitudes can be constructed from a double copy between (super-)Yang-Mills theory and a new gauge theory built entirely out of dimension-six operators. The latter theory is marginal in six dimensions and contains modes with a wrong-sign propagator, echoing the behavior of conformal gravity. The dimension-six Lagrangian is uniquely determined by demanding that its scattering amplitudes obey the color-kinematics duality. The conformal gravity amplitudes obtained from the double copy are compared with the Berkovits-Witten twistor string and shown to agree up to at least eight points in the MHV sector. Our construction can be generalized in a number of ways. Adding scalars to the dimension-six theory gives Maxwell-Weyl gravity, and further adding phi^3 self-interactions among these scalars gives Yang-Mills-Weyl gravity. The latter is identified with Witten's twistor string for maximal N=4 supersymmetry. Deforming the dimension-six theory by adding a Yang-Mills term, m^2 F^2, gives a gauge theory that interpolates between marginal D=6 and D=4 theories. The corresponding double copy gives an interpolation between conformal gravity and Einstein gravity.

42 pages, 3 figures, 12 Feynman rules

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Cited by in corpus (28)

• The Kerr-Schild double copy in curved spacetime
• Aspects of Scattering Amplitudes and Moduli Space Localization
• Heterotic and bosonic string amplitudes via field theory
• A new gauge-invariant double copy for heavy-mass effective theory
• Topology and Wilson lines: global aspects of the double copy
• Covariant Color-Kinematics Duality
• Extended solutions for the biadjoint scalar field
• Double copy structure and the flat space limit of conformal correlators in even dimensions
• Are all supergravity theories Yang-Mills squared?
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Composing Effective Prediction at Five Points
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• Conformal Symmetry in Field Theory and in Quantum Gravity
• Connecting the ambitwistor and the sectorized heterotic strings
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• N = 3 Conformal Supergravity in Four Dimensions
• New Worldsheet Formulae for Conformal Supergravity Amplitudes
• BCJ, worldsheet quantum algebra and KZ equations
• Ambitwistor Strings in Six and Five Dimensions
• Analytical amplitudes from numerical solutions of the scattering equations
• Non-Abelian gauged supergravities as double copies
• UV consistency conditions for CHY integrands
• Next-to-MHV Yang-Mills kinematic algebra
• The Weyl double copy from twistor space
• Inflation versus collapse in brane matter
• $p$-Branes with $Ad{S}_{p+1}$ vacuum as models of $R^2$ gravity