From Weyl to Cotton: The 3D Double Copy

From Weyl to Cotton: The 3D Double Copy

Recent developments in scattering amplitudes have enabled the construction of classical physics in terms of on-shell scattering amplitudes. Among the powerful tools that can be mapped over is the double copy relation between gauge theory and gravity. This has yielded a number of interesting results in classical physics, such as the Weyl double copy. Motivated by its success in 4D, interest has been reignited in 3D constructions, in particular topologically massive gauge and gravity theories, which can be related to 4D massless counterparts via dimensional reduction. In this talk, I will discuss how one can construct classical curvature spinors in such theories directly from massive three-particle amplitudes. I will elaborate on the double copy structure of these amplitudes and how, when this holds, one can show that the curvature spinors satisfy the Cotton double copy. Furthermore, I will discuss how this 3D cousin of the Weyl double copy can, under certain circumstances, be derived via dimensional reduction of the latter.