  We study and compute supersymmetric observables for line defects in 3d
$\mathcal{N}\ge4$ theories. Our setup is a novel supersymmetric configuration
involving line operators and local operators living on a linked circle. The
algebra of the local operators is described by a topological quantum mechanics.
For operators belonging to conserved current multiplets, we propose an exact
formula for their correlation functions based on a Ward identity for integrated
correlators. Our formula gives a general recipe to compute the bremsstrahlung
function for any $\frac{1}{3}$-BPS lines in $\mathcal{N}=6$ SCFTs. We apply our
relation to the $\frac{1}{2}$-BPS Wilson loop in the ABJM model, showing the
validity of previous computations. Furthermore, our construction allows us to
explore higher points correlators. As an example, we compute the two-point
function of the stress tensor multiplet correlators in ABJM theory in the
presence of the Wilson line. We also present some perturbative checks of our
formulae.
