Massive double copy in three spacetime dimensions

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.

Automated summary

Recent research on constructing a double copy of massive gauge fields has shown that the generic double copy is unphysical, but a new direction has been explored in three-dimensional spacetimes to obtain a sensible double copy of massive gauge fields. By requiring scattering amplitudes to satisfy a specific BCJ relation to avoid spurious poles at 5-points, it has been demonstrated that the amplitudes of Topologically Massive Yang-Mills satisfy this relation and that their double copy is Topologically Massive Gravity at three, four, and five-points.