Black hole singularity from OPE
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13130_2024_Article_24686.pdf
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Author(s)
Čeplak, Nejc
Liu, Hong
Parnachev, Andrei
Valach, Samuel
Date Issued
October 11, 2024
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Čeplak, N., Liu, H., Parnachev, A. et al. Black hole singularity from OPE. J. High Energ. Phys. 2024, 105 (2024).
Version
Final published version
Abstract
Eternal asymptotically AdS black holes are dual to thermofield double states in the boundary CFT. It has long been known that black hole singularities have certain signatures in boundary thermal two-point functions related to null geodesics bouncing off the singularities (bouncing geodesics). In this paper we shed light on the manifestations of black hole singularities in the dual CFT. We decompose the boundary CFT correlator of scalar operators using the Operator Product Expansion (OPE) and focus on the contributions from the identity, the stress tensor, and its products. We show that this part of the correlator develops singularities precisely at the points that are connected by bulk bouncing geodesics. Black hole singularities are thus encoded in the analytic behavior of the boundary correlators determined by multiple stress tensor exchanges. Furthermore, we show that in the limit where the conformal dimension of the operators is large, the sum of multi-stress-tensor contributions develops a branch point singularity as predicted by the geodesic analysis. We also argue that the appearance of complexified geodesics, which play an important role in computing the full correlator, is related to the contributions of the double-trace operators in the boundary CFT.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP10(2024)105
