Abstract
Lorentzian correlators of local operators exhibit surprising singularities in theories with gravity duals. These are associated with null geodesics in an emergent bulk geometry. We analyze singularities of the thermal response function dual to propagation of waves on the AdS Schwarzschild black hole background. We derive the analytic form of the leading singularity dual to a bulk geodesic that winds around the black hole. Remarkably, it exhibits a boundary group velocity larger than the speed of light, whose dual is the angular velocity of null geodesics at the photon sphere. The strength of the singularity is controlled by the classical Lyapunov exponent associated with the instability of nearly bound photon orbits. In this sense, the bulk-cone singularity can be identified as the universal feature that encodes the ubiquitous black hole photon sphere in a dual holographic CFT. To perform the computation analytically, we express the two-point correlator as an infinite sum over Regge poles, and then evaluate this sum using WKB methods. We also compute the smeared correlator numerically, which in particular allows us to check and support our analytic predictions. We comment on the resolution of black hole bulk-cone singularities by stringy and gravitational effects into black hole bulk-cone “bumps”. We conclude that these bumps are robust, and could serve as a target for simulations of black hole-like geometries in table-top experiments.
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Acknowledgments
We thank Antonio Antunes, David Berenstein, Stefano Giusto, Alba Grassi, Nima Lashkari, Raghu Mahajan, Vasiliy Makhalov, Andrei Parnachev, Hirosi Ooguri, Kyriakos Papadodimas, Elli Pomoni, Marcos Riojas, Rodolfo Russo, Eva Silverstein, Hao-Yu Sun, Aron Wall, and Zahra Zahraee for useful discussions. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 949077). The work of CI is partially supported by the Swiss National Science Foundation Grant No. 185723. The work of AL is partly supported by the National Science Foundation Grant No. 2307888.
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Dodelson, M., Iossa, C., Karlsson, R. et al. Black hole bulk-cone singularities. J. High Energ. Phys. 2024, 46 (2024). https://doi.org/10.1007/JHEP07(2024)046
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DOI: https://doi.org/10.1007/JHEP07(2024)046