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

TL;DR

This paper investigates bulk-defect-defect correlators in N=4 Super Yang-Mills with a Wilson line, revealing cancellations of transcendental terms at weak coupling and providing strong-coupling results through a combination of methods.

Contribution

It introduces a perturbative bootstrap approach for Wilson-line defect CFTs, combining non-perturbative constraints with explicit calculations at weak and strong coupling.

Findings

Transcendental terms cancel at next-to-leading order in weak coupling.

First strong-coupling results obtained using Witten diagrams and constraints.

Non-perturbative constraints significantly inform correlator structure.

Abstract

We study the correlators of bulk and defect half-BPS operators in $\mathcal{N}=4$ Super Yang-Mills theory with a Maldacena-Wilson line defect, focusing on the case involving one bulk and two defect local operators. We analyze the non-perturbative constraints on these correlators, which include a topological sector, pinching and splitting limits, and we compute a variety of bulk-defect-defect correlators up to next-to-leading order at weak coupling, surprisingly observing that transcendental terms cancel. Additionally, we provide results in the strong-coupling regime for the first two leading orders using a mixture of Witten diagrams and non-perturbative constraints.