’t Hooft loops and integrability

Abstract We consider the defect CFT defined by a ’t Hooft line embedded in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory. By explicitly quantizing around the given background we exactly reproduce a prediction from S-duality for the correlators between the ’t Hooft line and chiral primaries in the bulk and pave the way for higher loop analyses for non-protected operators. Furthermore, we demonstrate at the leading perturbative order that correlators between the ’t Hooft line and non-protected bulk operators can be efficiently computed using integrability. As a byproduct we find new integrable overlaps in sl $$ \mathfrak{sl} $$ (2) spin chains in different representations