New Relations for Three-Dimensional Supersymmetric Scattering Amplitudes

TL;DR

The paper investigates whether a color–kinematics duality known in higher dimensions extends to three-dimensional supersymmetric Chern–Simons matter theories. It demonstrates that six-point amplitudes in $\mathcal{N}=8$ SCS can be reorganized so kinematic factors satisfy three-algebra identities, enabling a double-copy to $\mathcal{N}=16$ three-dimensional supergravity. It provides concrete evidence that four- and six-point amplitudes in BLG/ABJM theories square to the amplitudes of $E_{8(8)}$ supergravity, and shows a consistent double-copy at these points using ABJM-derived numerators. The results suggest a hidden three-algebra structure in 3D gravity and motivate extending the construction to all loops and higher points.

Abstract

We provide evidence for a duality between color and kinematics in three-dimensional supersymmetric Chern-Simons matter theories. We show that the six-point amplitude in the maximally supersymmetric, N=8, theory can be arranged so that the kinematic factors satisfy the fundamental identity of three-algebras. We further show that the four- and six-point N=8 amplitudes can be "squared" into the amplitudes of N=16 three-dimensional supergravity, thus providing evidence for a hidden three-algebra structure in the dynamics of the supergravity.

Figures (2)

• Figure 1: Six point quartic diagram.
• Figure 2: Graphical expression of the fundamental identity.