Abstract
We prepare an excited finite temperature state in \( \mathcal{N} \) = 4 SYM by means of a Euclidean path integral with a relevant deformation. The deformation explicitly breaks imaginary-time translations along the thermal circle whilst preserving its periodicity. We then study how the state relaxes to thermal equilibrium in real time. Computations are performed using real-time AdS/CFT, by constructing novel mixed-signature black holes in numerical relativity corresponding to Schwinger-Keldysh boundary conditions. These correspond to deformed cigar geometries in the Euclidean, glued to a pair of dynamical spacetimes in the Lorentzian.
The maximal extension of the Lorentzian black hole exhibits a ‘causal shadow’, a bulk region which is spacelike separated from both boundaries. We show that causal shadows are generic in path-integral prepared states where imaginary-time translations along the thermal circle are broken.
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Acknowledgments
It is a pleasure to thank Adam Bzowski, Carsten Gundlach, Michal Heller, Romuald Janik, Pavel Kovtun and Toby Wiseman for discussions. B.W. thanks KITP Santa Barbara for hospitality during the programme “The Many Faces of Relativistic Fluid Dynamics”. C.P. acknowledges support from a Royal Society - Science Foundation Ireland University Research Fellowship via grant URF/R1/211027. B.W. is supported by a Royal Society University Research Fellowship and in part by the Science and Technology Facilities Council (Consolidated Grant ‘Exploring the Limits of the Standard Model and Beyond’). This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958.
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Pantelidou, C., Withers, B. Black hole excited states from broken translations in Euclidean time. J. High Energ. Phys. 2024, 152 (2024). https://doi.org/10.1007/JHEP01(2024)152
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DOI: https://doi.org/10.1007/JHEP01(2024)152