Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories

TL;DR

This paper demonstrates that three-dimensional supergravity amplitudes can be derived from double copies of specific gauge theories, revealing the structure of these amplitudes and their relation to color-kinematics duality.

Contribution

It establishes a double-copy construction for 3D supergravity amplitudes using three-algebra and two-algebra gauge theories, extending the color-kinematics duality to three dimensions.

Findings

Supergravity amplitudes obtained from double copies of gauge theories.

Only helicity-conserving 4D amplitudes have nonvanishing 3D descendants.

Explicit verification at four and six points for various supersymmetries.

Abstract

We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or that of two-algebra super-Yang-Mills theory, when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions; implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N=12,10,8 supergravity theories and discuss its validity for all multiplicity.