  We study the large charge sector of the defect CFT defined by the half-BPS
Wilson loop in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory.
Specifically, we consider correlation functions of two large charge insertions
and several light insertions in the double-scaling limit where the 't Hooft
coupling $\lambda$ and the large charge $J$ are sent to infinity, with the
ratio $J/\sqrt{\lambda}$ held fixed. They are holographically dual to the
expectation values of light vertex operators on a classical string solution
with large angular momentum, which we evaluate in the leading large $J$ limit.
We also compute the two-point function of large charge insertions by evaluating
the on-shell string action, supplemented by the boundary terms that generalize
the one introduced by Drukker, Gross and Ooguri for the Wilson loop without
insertions. For a special class of correlation functions, we reproduce the
string results from field theory by using supersymmetric localization. The
results are given by correlation functions in an "emergent" matrix model whose
matrix size is proportional to $J$ and whose spectral curve coincides with that
of the classical string. Similar matrix models appeared in the study of
extremal correlators in rank-1 $\mathcal{N}=2$ superconformal field theories,
but our results hold also for non-extremal cases.
