On protected defect correlators in 3d $$ \mathcal{N} $$ ≥ 4 theories

Abstract

We study and compute supersymmetric observables for line defects in 3d $$ \mathcal{N} $$ N ≥ 4 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 $$ \frac{1}{3} $$ 1 3 -BPS lines in $$ \mathcal{N} $$ N = 6 SCFTs. We apply our relation to the $$ \frac{1}{2} $$ 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.