Conformal Gravity from Gauge Theory

TL;DR

This paper constructs scattering amplitudes for conformal gravity using a double copy approach from gauge theories, revealing new connections with twistor string theory and interpolations between gravity theories.

Contribution

It introduces a novel gauge theory built from dimension-six operators to generate conformal gravity amplitudes via the double copy method.

Findings

Conformal gravity amplitudes match twistor string results up to eight points.

A new gauge theory with dimension-six operators is constructed and uniquely determined.

The framework allows interpolations between conformal and Einstein gravity.

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.