Massive Double Copy in Three Spacetime Dimensions

TL;DR

This paper demonstrates a consistent double copy construction for massive gauge fields in three dimensions, leading to Topologically Massive Gravity, by leveraging special kinematics and minimal BCJ relations.

Contribution

It introduces a new approach to obtain a physical double copy of massive gauge fields in three dimensions using simplified BCJ relations.

Findings

Double copy of Topologically Massive Yang-Mills yields Topologically Massive Gravity.

Amplitudes satisfy a single BCJ relation to avoid unphysical poles.

Method applies to three, four, and five-point scattering amplitudes.

Abstract

Recent explorations on how to construct a double copy of massive gauge fields have shown that, while any amplitude can be written in a form consistent with colour-kinematics duality, the double copy is generically unphysical. In this paper, we explore a new direction in which we can obtain a sensible double copy of massive gauge fields due to the special kinematics in three-dimensional spacetimes. To avoid the appearance of spurious poles at 5-points, we only require that the scattering amplitudes satisfy one BCJ relation. We show that the amplitudes of Topologically Massive Yang-Mills satisfy this relation and that their double copy at three, four, and five-points is Topologically Massive Gravity.