# Towards the exact Bremsstrahlung function of ABJM theory

## TL;DR

This paper computes the three-loop Bremsstrahlung function for the 1/2-BPS cusp in ABJM theory, providing evidence for an exact expression based on advanced perturbative techniques and theoretical conjectures.

## Contribution

It presents the first three-loop calculation of the Bremsstrahlung function in ABJM theory, including color subleading corrections, and confirms a conjectured exact formula.

## Key findings

- Results agree with the conjectured exact expression.
- The calculation passes nontrivial tests like exponentiation.
- The approach simplifies the evaluation using HQET and BPS conditions.

## Abstract

We present the three-loop calculation of the Bremsstrahlung function associated to the 1/2-BPS cusp in ABJM theory, including color subleading corrections. Using the BPS condition we reduce the computation to that of a cusp with vanishing angle. We work within the framework of heavy quark effective theory (HQET) that further simplifies the analytic evaluation of the relevant cusp anomalous dimension in the near-BPS limit. The result passes nontrivial tests, such as exponentiation, and is in agreement with the conjecture made in [1] for the exact expression of the Bremsstrahlung function, based on the relation with fermionic latitude Wilson loops.