Perturbative bootstrap of the Wilson-line defect CFT: Multipoint correlators

We study the defect CFT associated with the half-BPS Wilson line in $\mathcal{N}=4$ Super Yang-Mills theory in four dimensions. Using a perturbative bootstrap approach, we derive new analytical results for multipoint correlators of protected defect operators at large $N$ and weak coupling. At next-to-next-to-leading order, we demonstrate that the simplest five- and six-point functions are fully determined by non-perturbative constraints – which include superconformal symmetry, crossing symmetry, and the pinching of operators to lower-point functions – as well as by a single integral, known as the train track integral. Additionally, we present new analytical results for the four-point functions $⟨1122⟩$ and $⟨1212⟩$.