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.
Highlights
This seems to be too restrictive, but it could be expected since the spectral conditions appear to have been modeled from the knowledge that Kaluza-Klein theories have a sensible double copy given that they satisfy colour-kinematics duality for the massless theories in higher dimensions
The special kinematics arising in a three-dimensional spacetime allow us to construct a well-defined massive double copy that does not require a tower of massive states
We have shown how the spurious poles that generically appear in 5-point amplitudes can be avoided with a single BCJ relation
Summary
We review the double copy construction for scattering amplitudes with matrix notation, as introduced in [99], which is useful to understand the issues that arise when including massive gauge fields. We have a single Jacobi identity, cs + ct + cu = 0, so M has only one non zero row equal to [1, 1, 1] and D = diag(s − m2, t − m2, u − m2). In this case M n = (ns + nt + nu, 0, 0), so U = ns + nt + nu and A is 1 × 1 matrix A = s − m2 + t − m2 + u − m2 = m2. We analyze the special features that arise for 3D spacetimes
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