ABJM $\theta$-Bremsstrahlung at four loops and beyond: non-planar corrections

TL;DR

This paper extends the four-loop weak coupling calculation of the ABJM Bremsstrahlung function to include non-planar corrections, supporting a conjecture linking it to supersymmetric Wilson loops computed via localization.

Contribution

It provides the first non-planar correction computation for the ABJM Bremsstrahlung function at four loops, validating a conjecture relating it to localized Wilson loops.

Findings

Agreement between perturbative and localization results including non-planar corrections

Supports the conjecture beyond the planar limit

Extends weak coupling calculations to non-planar contributions

Abstract

We consider the Bremsstrahlung function associated to a 1/6-BPS Wilson loop in ABJM theory, with a cusp in the couplings to scalar fields. We non-trivially extend its recent four-loop computation at weak coupling to include non-planar corrections. We have recently proposed a conjecture relating this object to supersymmetric circular Wilson loops with multiple windings, which can be computed via localization. We find agreement between this proposal and the perturbative computation of the Bremsstrahlung function, including color sub-leading corrections. This supports the conjecture and hints at its validity beyond the planar approximation.