Conformal Gravity from Gauge Theory
Authors: Henrik Johansson and Josh Nohle Preprint number UUITP-21/17 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.
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Our construction can be generalized in a number of ways. Adding scalars to the dimension-six theory gives Maxwell-Weyl gravity, and further adding φ^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.