# Exact Bremsstrahlung functions in ABJM theory

## TL;DR

This paper derives exact formulas for Bremsstrahlung functions in ABJM theory's Wilson lines using superconformal defect techniques, revealing new relations and providing results compatible with integrability.

## Contribution

It proves a conjectured relation between Bremsstrahlung functions for 1/6 BPS Wilson lines and derives exact expressions for 1/2 BPS cases in ABJM theory.

## Key findings

- Exact relation between $B^{ heta}_{1/6}$ and $B^{{ heta}_{1/6}$ derived.
- Closed-form expression for Bremsstrahlung function of 1/2 BPS Wilson line.
- Analysis of protected defect supermultiplets and their correlators.

## Abstract

In this paper we study the Bremsstrahlung functions for the 1/6 BPS and the 1/2 BPS Wilson lines in ABJM theory. First we use a superconformal defect approach to prove a conjectured relation between the Bremsstrahlung functions associated to the geometric ($B^{\varphi}_{1/6}$) and R-symmetry ($B^{\theta}_{1/6}$) deformations of the 1/6 BPS Wilson line. This result, non-trivially following from a defect supersymmetric Ward identity, provides an exact expression for $B^{\theta}_{1/6}$ based on a known result for $B^{\varphi}_{1/6}$. Subsequently, we explore the consequences of this relation for the 1/2 BPS Wilson line and, using the localization result for the multiply wound Wilson loop, we provide an exact closed form for the corresponding Bremsstrahlung function. Interestingly, for the comparison with integrability, this expression appears particularly natural in terms of the conjectured interpolating function $h(\lambda)$. During the derivation of these results we analyze the protected defect supermultiplets associated to the broken symmetries, including their two- and three-point correlators.