Yangian Invariant Scattering Amplitudes in Supersymmetric Chern-Simons Theory

TL;DR

This work extends the Arkani-Hamed generating-function program from 4D N=4 super-Yang-Mills to 3D N=6 super-Chern-Simons theory by introducing a generating function L_{2k} for SCS_6 amplitudes. It demonstrates that L_{2k} is superconformally invariant and, crucially, Yangian invariant, suggesting integrability in the planar sector. The construction reproduces known tree-level amplitudes (notably the 4-point case) and reveals connections to dual superconformal symmetry and momentum-twistor formulations, while outlining open issues on contours, recursion, and a complete Yangian proof. The results point toward a unifying Grassmannian-like picture for SCS_6 amplitudes and invite further work to establish a full duality with momentum-space dualities and to generalize to higher points. The work thus strengthens the evidence that Yangian symmetry governs the structure of scattering amplitudes in this class of 3D theories and provides a concrete generating-function framework for future explorations.

Abstract

We propose a generating function for scattering amplitudes of N=6 super-Chern-Simons theory which parallels a recent work on N=4 super-Yang-Mills theory by Arkani-Hamed et al. Our result suggests that the scattering amplitudes of the super-Chern-Simons theory exhibit Yangian invariance.