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We study three-point functions of operators on the $1/2$ BPS Wilson loop inplanar $\mathcal{N}=4$ super Yang-Mills theory. The operators we consider are"defect changing operators", which change the scalar coupled to the Wilsonloop. We first perform the computation at two loops in general set-ups, andthen study a special scaling limit called the ladders limit, in which thespectrum is known to be described by a quantum mechanics with theSL(2,$\mathbb{R}$) symmetry. In this limit, we resum the Feynman diagrams usingthe Schwinger-Dyson equation and determine the structure constants at all orderin the rescaled coupling constant. Besides providing an interesting solvableexample of defect conformal field theories, our result gives invaluable datafor the integrability-based approach to the structure constants.

Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop