Exact Bremsstrahlung functions in ABJM theory

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.