Universal Constraints for Conformal Line Defects

TL;DR

This paper introduces a new framework for deriving integral constraints on correlators in conformal line defects, leveraging ambient-space conformal symmetry, validated through examples and extended with new predictions.

Contribution

It presents a novel method for deriving integral constraints on defect correlators using ambient-space symmetry, with validation and new predictions.

Findings

Validated constraints against existing four-point function data.

Extended understanding with new predictions for defect correlators.

Demonstrated applicability across multiple examples.

Abstract

We present a novel framework for deriving integral constraints for correlators on conformal line defects. These constraints emerge from the non-linearly realized ambient-space conformal symmetry. To validate our approach, we examine several examples and compare them against existing data for the four-point function of the displacement operator. Additionally, we provide a few new predictions that extend the current understanding of these correlators.