A note on amplitudes in N=6 superconformal Chern-Simons theory

TL;DR

This paper explores the relationship between tree-level and one-loop superamplitudes in ABJM theory, revealing new connections and providing simplified calculations for six- and eight-point amplitudes.

Contribution

It establishes a novel link between superamplitudes and leading singularities in ABJM theory, simplifying amplitude calculations and highlighting similarities with four-dimensional gauge theories.

Findings

Derived a relation between superamplitudes and leading singularities.

Re-derived the six-point superamplitude using new methods.

Calculated the eight-point one-loop superamplitude in ABJM theory.

Abstract

We establish a connection between tree-level superamplitudes in ABJM theory and leading singularities associated to special three-particle cuts of one-loop superamplitudes where one of the tree amplitudes entering the cut is a four-point amplitude. Using these relations, we show that certain intriguing similarities between one-loop and tree-level superamplitudes observed recently become completely manifest. This connection is reminiscent of a similar relation in the maximally supersymmetric gauge theory in four dimensions, where the sum of two-mass hard and one-mass box coefficients of a one-loop amplitude equals the corresponding tree-level amplitude. As an application, we present a very simple re-derivation of the six-point superamplitude and calculate the eight-point superamplitude at one loop in ABJM theory.