Mini-twistors and the Cotton Double Copy

TL;DR

This paper employs twistor methods to derive the Cotton double copy in position space, linking minitwistor data with spacetime solutions, and explores its applicability to different solution types using scattering amplitudes and anyons.

Contribution

It provides a twistor-based derivation of the Cotton double copy and extends understanding of its applicability to non-type N solutions.

Findings

Cotton double copy arises from minitwistor data.

Position-space double copy valid for type N solutions.

Twistor space double copy extends to non-type N solutions with anyons.

Abstract

The double copy relates quantities in gauge, gravity and related theories. A well-known procedure for relating exact classical solutions is the Weyl double copy in four spacetime dimensions, and a three-dimensional analogue of this -- the Cotton double copy -- has recently been found for topologically massive gauge theory and gravity. In this paper, we use twistor methods to provide a derivation of the position-space Cotton double copy, where this is seen to arise from combining appropriate data in so-called minitwistor space. Our methods rely on a massive generalisation of the Penrose transform linking spacetime fields with cohomology classes in minitwistor space. We identify the relevant transform from the twistor literature, but also show that it naturally arises from considering scattering amplitudes in momentum space. We show that the Cotton double copy in position space is only valid for type N solutions, but that a simple twistor space double copy is possible for non-type N solutions, where we use anyons to illustrate our arguments.