Correlation functions of BCFT

TL;DR

The paper analyzes boundary conformal field theories (BCFT) in two dimensions by leveraging the 2D conformal group to constrain correlation functions in both free space and semi-infinite domains with boundaries. It builds the representations of the 2D conformal algebra via two Witt copies, identifies primary fields with weights $(h,\bar h)$, and derives explicit forms for two-point and three-point functions under various boundary conditions. In semi-infinite geometries, the authors show how boundaries modify standard power-law correlators, introducing boundary-dependent functions and multi-term combinations that encode Neumann or Dirichlet constraints, and they demonstrate agreement with gravity dual results in the appropriate limit. Overall, the work provides a systematic conformal-field-theoretic framework for BCFT correlators across multiple boundary configurations, with implications for holographic BCFT and boundary-induced operator spectra.

Abstract

Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) on manifolds with a boundary. We can use conformal symmetry to constrain correlation functions of conformal invariant fields. We compute two-point and three-point functions of conformal invariant fields which live in semi-infinite space. For a situation with a boundary condition in surface $z=\bar{z}$ ($t=0$), the results agree with gravity dual results. We also explore representations of conformal group in two dimensions.