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

TL;DR

This paper develops a perturbative bootstrap method to analytically compute multipoint correlators of protected operators in the defect CFT of the Wilson line in N=4 Super Yang-Mills, revealing constraints at higher orders and new explicit results.

Contribution

It introduces a perturbative bootstrap framework for defect CFTs, deriving analytical multipoint correlators at large N and weak coupling, including non-perturbative constraints and explicit results.

Findings

Five- and six-point functions are fully determined by symmetry and integral constraints.

New analytical results for four-point functions $raket{1122}$ and $raket{1212}$.

Higher-point functions constrained by superconformal symmetry, crossing, and operator pinching.

Abstract

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 $\langle 1122 \rangle$ and $\langle 1212 \rangle$.