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Improved image method for a holographic description of conical defects

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Abstract

The geodesics prescription in the holographic approach in the Lorentzian signature is applicable only for geodesics connecting spacelike-separated points at the boundary because there are no timelike geodesics that reach the boundary. Also, generally speaking, there is no direct analytic Euclidean continuation for a general background, such as a moving particle in the AdS space. We propose an improved geodesic image method for two-point Lorentzian correlators that is applicable for arbitrary time intervals when the space–time is deformed by point particles. We show that such a prescription agrees with the case where the analytic continuation exists and also with the previously used prescription for quasigeodesics. We also discuss some other applications of the improved image method: holographic entanglement entropy and multiple particles in the AdS3 space.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    I. Ya. Aref’eva, M. A. Khramtsov & M. D. Tikhanovskaya

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  1. I. Ya. Aref’eva
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  2. M. A. Khramtsov
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  3. M. D. Tikhanovskaya
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Correspondence to I. Ya. Aref’eva.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 189, No. 2, pp. 296–311, November, 2016.

Section 3 was done by M. A. Khramtsov, and the remaining sections were done by I. Ya. Aref’eva and M. D. Tikhanovskaya. The research of I. Ya. Aref’eva and M. D. Tikhanovskaya was performed at the Steklov Mathematical Institute of Russian Academy of Sciences and supported by a grant from the Russian Science Foundation (Project No. 14-11-00687).

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Aref’eva, I.Y., Khramtsov, M.A. & Tikhanovskaya, M.D. Improved image method for a holographic description of conical defects. Theor Math Phys 189, 1660–1672 (2016). https://doi.org/10.1134/S0040577916110106

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