Structure of Holographic BCFT Correlators from Geodesics

TL;DR

This paper analyzes holographic BCFT correlators using geodesic approximation, revealing boundary effects, phase transitions, and novel boundary operators, with results validated against exact calculations.

Contribution

It introduces a geodesic-based method for computing BCFT correlators in holography, including boundary reflections and novel boundary operator insights.

Findings

Agreement between geodesic and exact 1-point functions

Identification of a phase transition in 2-point functions

Discovery of anomalous boundary-localized operators

Abstract

We compute correlation functions, specifically 1-point and 2-point functions, in holographic boundary conformal field theory (BCFT) using geodesic approximation. The holographic model consists of a massive scalar field coupled to a Karch-Randall brane -- a rigid boundary in the bulk AdS space. Geodesic approximation requires the inclusion of paths reflecting off of this brane, which we show in detail. For the 1-point function, we find agreement between geodesic approximation and the harder $\Delta$-exact calculation, and we give a novel derivation of boundary entropy using the result. For the 2-point function, we find a factorization phase transition and a mysterious set of anomalous boundary-localized BCFT operators. We also discuss some puzzles concerning these operators.