Structure of Holographic BCFT Correlators from Geodesics

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.

arXiv comment17 pages (including appendices) + references, 11 figures; v3: fixed additional typos, matches version to appear in PRD

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• BCFT and Islands in Two Dimensions
• Sailing past the End of the World and discovering the Island
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• Defect extremal surfaces for entanglement negativity
• Universal Dynamics of Heavy Operators in Boundary CFT${}_2$
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