All one-loop amplitudes in N=6 superconformal Chern-Simons theory

TL;DR

This paper derives a comprehensive formula for one-loop amplitudes in N=6 superconformal Chern-Simons theory, connecting multi-particle factorisation with recursive diagrams and revealing anomalous contributions.

Contribution

It introduces a general formula for one-loop amplitudes in ABJM theory and a recursion relation for supercoefficients, linking loop amplitudes to tree-level recursive diagrams.

Findings

Derived a general multi-particle factorisation formula for one-loop amplitudes.

Established a recursion relation reducing supercoefficients to tree-level diagrams.

Identified anomalous non-factorising contributions in the amplitude structure.

Abstract

We exploit a recently found connection between special triple-cut diagrams and tree-level recursive diagrams to derive a general formula capturing the multi-particle factorisation of arbitrary one-loop amplitudes in the ABJM theory. This formula contains certain anomalous contributions which are reminiscent of the so-called non-factorising contributions appearing in the factorisation of one-loop amplitudes in four-dimensional gauge theory. In the second part of the paper we derive a recursion relation for the supercoefficients of one-loop amplitudes in ABJM theory. By applying this recursion relation, any one-loop supercoefficient can be reduced to special triple-cut diagrams involving at least one four-point tree amplitude. In turn, this implies that any one-loop supercoefficient can be derived from tree-level recursive diagrams.