Multipoint correlators on the supersymmetric Wilson line defect CFT

TL;DR

This paper develops a recursive method to compute multipoint correlators of protected scalars on the supersymmetric Wilson line in N=4 SYM at weak coupling, revealing differential constraints that extend superconformal Ward identities.

Contribution

It introduces an explicit recursion relation for arbitrary n-point correlators of protected operators, including higher R-charge operators, in the defect CFT setting.

Findings

Derived explicit formulas for up to six-point correlators.

Identified differential operators annihilating all correlators.

Proposed these operators as non-perturbative constraints extending Ward identities.

Abstract

We study multipoint correlators of protected scalars on the Maldacena-Wilson line in $\mathcal{N}=4$ SYM. Working at weak coupling in the planar limit, we derive an explicit recursion relation that captures next-to-leading order correlators with an arbitrary number of insertions of the fundamental scalar field. By pinching fundamental scalars together, we can build composite protected operators with higher values of the R-charge. Our result then encompasses arbitrary $n$-point correlators of protected operators with arbitrary weight. As a demonstration of our method, we give explicit formulae for correlators with up to six points. Using these results we observe that all our correlators are annihilated by a special class of differential operators. We conjecture that these differential operators are non-perturbative constraints and can be considered a multipoint extension of the superconformal Ward identities satisfied by four-point functions.