Scattering Amplitudes and The Cotton Double Copy

TL;DR

This paper explores the relationship between scattering amplitudes and the Cotton double copy in three-dimensional topologically massive theories, revealing how curvature spinors relate through a double copy structure and dimensional reduction.

Contribution

It introduces the construction of classical curvature spinors in topologically massive theories and demonstrates their connection via the Cotton double copy, extending the double copy concept to three dimensions.

Findings

Curvature spinors can be expressed in terms of massive three-particle amplitudes.

The Cotton double copy relates curvature spinors in topologically massive gravity and gauge theory.

Dimensional reduction links the Cotton double copy to the Weyl double copy.

Abstract

We construct classical curvature spinors in topologically massive gauge theory and topologically massive gravity, expressed in terms of massive three-particle amplitudes. We show that when the amplitudes double copy, the curvature spinors satisfy the Cotton double copy, the three-dimensional cousin of the Weyl double copy. Furthermore, we show that under certain circumstances the Cotton double copy can be derived via a dimensional reduction of the Weyl double copy.