Method of images in defect conformal field theories

TL;DR

This paper introduces a generalized image method for higher-dimensional defect conformal field theories, relating their correlation functions to those in defect-free conformal field theories, thus enabling new analytical approaches.

Contribution

It proposes a novel prescription linking DCFT correlation functions to those in standard CFTs, extending the classical image method to higher dimensions and defects.

Findings

Correlation functions in DCFTs can be represented by doubled correlators in ancillary CFTs.

The method is validated for scalar operators by matching conformal symmetry constraints.

Potential to explore new aspects of DCFTs using conventional CFT techniques.

Abstract

We propose a prescription for describing correlation functions in higher-dimensional defect conformal field theories (DCFTs) by those in ancillary conformal field theories (CFTs) without defects, which is a vast generalization of the image method in two-dimensional boundary CFTs. A correlation function of $n$ operators inserted away from a defect in a DCFT is represented by a correlation function of $2n$ operators in the ancillary CFT, each pair of which is placed symmetrically with respect to the defect. For scalar operators, we establish the correspondence by matching the constraints on correlation functions imposed by conformal symmetry on both sides. Our method has potential to shed light on new aspects of DCFTs from the viewpoint of conventional CFTs.