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

A bstract We study the defect CFT associated with the half-BPS Wilson line in $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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⟩.