  We perform exact computations of correlation functions of 1/2-BPS local
operators and protected operator insertions on the 1/8-BPS Wilson loop in
$\mathcal{N}=4$ SYM. This generalizes the results of our previous paper
arXiv:1802.05201, which employs supersymmetric localization, OPE and the
Gram-Schmidt process. In particular, we conduct a detailed analysis for the
1/2-BPS circular (or straight) Wilson loop in the planar limit, which defines
an interesting nontrivial defect CFT. We compute its bulk-defect structure
constants at finite 't Hooft coupling, and present simple integral expressions
in terms of the $Q$-functions that appear in the Quantum Spectral Curve---a
formalism originally introduced for the computation of the operator spectrum.
The results at strong coupling are found to be in precise agreement with the
holographic calculation based on perturbation theory around the AdS$_2$ string
worldsheet, where they correspond to correlation functions of open string
fluctuations and closed string vertex operators inserted on the worldsheet.
Along the way, we clarify several aspects of the Gram-Schmidt analysis which
were not addressed in the previous paper. In particular, we clarify the role
played by the multi-trace operators at the non-planar level, and confirm its
importance by computing the non-planar correction to the defect two-point
function. We also provide a formula for the first non-planar correction to the
defect correlators in terms of the Quantum Spectral Curve, which suggests the
potential applicability of the formalism to the non-planar correlation
functions.
