Correlation functions of boundary and defect conformal field theories

TL;DR

This paper uses holography to compute correlation functions in boundary and defect conformal field theories, revealing how boundary conditions and boundary entropy influence these functions with exact results.

Contribution

It provides a holographic framework for calculating boundary and defect CFT correlation functions, including cases with nontrivial boundary entropy, without relying on image operators.

Findings

Reproduces known boundary CFT correlation functions holographically.

Calculates correlation functions with nontrivial boundary entropy.

Derives exact bulk-to-defect two-point function coefficients.

Abstract

Applying the holographic method, we investigate correlation functions of boundary and defect conformal field theories. To describe boundary conformal field theory, we consider an end of the world brane in an asymptotic AdS space which behaves as a boundary in the dual conformal field theory. In this holographic setup, we calculate correlation functions involving the reflection effect at the boundary. We show that, when the end of the world brane has no degrees of freedom, the holographic calculation reproduces the correlation functions known in the boundary conformal field theory. When the boundary has nontrivial boundary entropy, we calculate one- and two-point functions nontrivially relying on the boundary entropy. We further study correlation functions of defect conformal field theory after introducing a $p$-brane. We directly derive a bulk-to-defect two-point function without introducing an image operator and determine the coefficient of the two-point function exactly in the holographic setup.