Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve

We study the anomalous dimension of the cusped Maldacena-Wilson line in planar $\mathcal{N} = 4$ Yang-Mills theory with scalar insertions using the Quantum Spectral Curve (QSC) method. In the straight line limit we interpret the excited states of the QSC as insertions of scalar operators coupled to the line. Such insertions were recently intensively studied in the context of the one-dimensional defect CFT. We compute a five-loop perturbative result analytically at weak coupling and the first four orders in the $1/\sqrt\lambda$ expansion at strong coupling, confirming all previous analytic results. In addition, we find the non-perturbative spectrum numerically and show that it interpolates smoothly between the weak and strong coupling predictions.