Two-loop Sudakov Form Factor in ABJM

TL;DR

This paper calculates the two-loop Sudakov form factor in ABJM theory using unitarity, revealing a non-planar integral structure and confirming known infrared divergence properties.

Contribution

It provides the first explicit computation of the two-loop Sudakov form factor in ABJM theory, including non-planar contributions, and explores properties of related three-dimensional integrals.

Findings

The two-loop Sudakov form factor is expressed by a single non-planar tensor integral.

The result matches the expected infrared divergences of two-loop amplitudes in ABJM.

Properties of related three-dimensional integral functions are discussed.

Abstract

We compute the two-loop Sudakov form factor in three-dimensional N=6 superconformal Chern-Simons theory, using generalised unitarity. As an intermediate step, we derive the non-planar part of the one-loop four-point amplitude in terms of box integrals. Our result for the Sudakov form factor is given by a single non-planar tensor integral with uniform degree of transcendentality, and is in agreement with the known infrared divergences of two-loop amplitudes in ABJM theory. We also discuss a number of interesting properties satisfied by related three-dimensional integral functions.