Bootstrapping the half-BPS line defect CFT in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at strong coupling

We consider the one-dimensional (1D) conformal field theory defined by the half-BPS Wilson line in planar $\mathcal{N}=4$ super Yang-Mills. Using analytic bootstrap methods we derive the four-point function of the superdisplacement operator at fourth order in a strong coupling expansion. Via AdS/CFT, this corresponds to the first three-loop correlator in anti–de Sitter ever computed. To do so we address the operator mixing problem by considering a family of auxiliary correlators. We further extract the anomalous dimension of the lightest nonprotected operator and find agreement with the integrability-based numerical result of Grabner, Gromov, and Julius.