Holographic Dual to Conical Defects III: Improved Image Method

Abstract

The geodesics prescription in holographic approach in Lorentzian signature is valid only for geodesics which connect spacelike-separated points at the boundary, since there are no timelike geodesics which reach the boundary. There is also no straightforward analytic Euclidean continuation for a general background, such as e. g. moving particle in AdS. We propose an improved geodesic image method for two-point Lorentzian correlators which is valid for arbitrary time intervals in case of the bulk spacetime deformed by point particles. We illustrate that our prescription is consistent with the case when the analytic continuation exists and with the quasigeodesics prescription used in previous work. We also discuss some other applications of the improved image method, such as holographic entanglement entropy and multiple particles in AdS3.

18 pages, 9 figures. v2: minor corrections, references added. Published in Theor. Math. Phys. under the title "Improved image method for holographic description of conical defects"

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• Aspects of Holography in Conical $Ad{S}_3$
• The landscape of complexity measures in 2D gravity
• How is the Presence of Horizons and Localized Matter Encoded in the Entanglement Entropy?
• Composite AdS geodesics for CFT correlators and timelike entanglement entropy
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