Method of images in defect conformal field theories

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.

6 pages, 3 figures; v3: published version

References in corpus (4)

• Conformal collider physics: Energy and charge correlations
• Boundary Conformal Field Theory and a Boundary Central Charge
• Displacement Operators and Constraints on Boundary Central Charges
• Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects

Cited by in corpus (5)

• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Boundary criticality for the Gross-Neveu-Yukawa models
• Conformal Defects in Neural Network Field Theories