Notes on flat-space limit of holographic defect correlators in position space

TL;DR

This paper investigates the flat-space limit of holographic defect correlators in position space, establishing a formula that connects these correlators to flat-space scattering form factors, and confirms its consistency with Mellin space conjectures.

Contribution

It derives a position space formula for the flat-space limit of defect correlators and demonstrates its equivalence to a Mellin space conjecture, tested in various theories.

Findings

Position space formula relates defect correlators to flat-space form factors.

The formula is shown to be equivalent to a Mellin space conjecture.

Results are validated in multiple nontrivial theories.

Abstract

We study the large AdS radius limit of correlation functions in holographic defect CFTs. For two-point functions of operators inserted away from the defect, we derive a position space formula relating a certain scaling limit of the correlators to the flat-space scattering form factors. We show that our position space prescription is equivalent to the flat-space limit formula recently conjectured in Mellin space and also test our result in a few nontrivial theories.