Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory

TL;DR

This paper introduces a recursion relation for tree-level amplitudes in ABJM theory, demonstrating dual superconformal symmetry and validating results through multiple computational methods.

Contribution

It proposes a novel recursion relation for three-dimensional Chern-Simons-matter theories and proves dual superconformal symmetry at tree level.

Findings

Recursion relation valid for all tree-level superamplitudes

Matching of computed amplitudes with Feynman and Grassmannian methods

Extension of dual superconformal symmetry to loop amplitudes

Abstract

We propose a recursion relation for tree-level scattering amplitudes in three-dimensional Chern-Simons-matter theories. The recursion relation involves a complex deformation of momenta which generalizes the BCFW-deformation used in higher dimensions. Using background field methods, we show that all tree-level superamplitudes of the ABJM theory vanish for large deformations, establishing the validity of the recursion formula. Furthermore, we use the recursion relation to compute six-point and eight-point component amplitudes and match them with independent computations based on Feynman diagrams or the Grassmannian integral formula. As an application of the recursion relation, we prove that all tree-level amplitudes of the ABJM theory have dual superconformal symmetry. Using generalized unitarity methods, we extend this symmetry to the cut-constructible parts of the loop amplitudes.