On protected defect correlators in 3d N ≥ 4 theories

We study and compute supersymmetric observables for line defects in 3dN >= 4theories. 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 brem sstrah lung function for any1/3-BPS lines in N= 6SCFTs. We apply our relation to the1/2-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