Abstract
In this note, we resolve an apparent obstacle to string/M theory realizations of dS observer patch holography, finding a new role for averaging in quantum gravity. The solvable \( T\overline{T} \)(+Λ2) deformation recently provided a detailed microstate count of the dS3 cosmic horizon, reproducing the refined Gibbons-Hawking entropy computed by Anninos et al. along with the correct radial bulk geometry. On the gravity side, the deformation brings in the boundary to just outside a black hole horizon, where it is indistinguishable from the dS cosmic horizon, enabling a continuous passage to a bounded patch of dS. In string/M theory, the relationship between AdS/CFT and dS involves uplifts that change the internal topology, e.g. replacing an internal sphere \( \mathbbm{S} \) with an internal hyperbolic space ℍ (and incorporating varying warp and conformal factors). We connect these two approaches, noting that the differences in the extra dimensions between AdS black hole and dS solutions are washed out by internal averaging in the presence of a timelike boundary skirting the horizon. This helps to motivate a detailed investigation into the possibility of such timelike boundaries in (A)dS solutions of string/M theory, and we take initial steps toward suitable generalizations of Liouville walls as one approach.
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Acknowledgments
I would like to thank G. Torroba and S. Yang for comments on the manuscript. I am grateful to the authors of [2] and the organizers and participants of the Corfu 2022 Workshop ‘Quantum features of a de Sitter Universe’ for many useful discussions. I am grateful to them and Shoaib Akhtar, Gauri Batra, G. Bruno De Luca, Alex Frenkel, Raghu Mahajan, Steve Shenker, Lenny Susskind, and Zhenbin Yang for useful remarks and/or ongoing collaboration on this topic. This work is supported in part by a Simons Investigator award and National Science Foundation grant PHY-2014215.
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Silverstein, E. Black hole to cosmic horizon microstates in string/M theory: timelike boundaries and internal averaging. J. High Energ. Phys. 2023, 160 (2023). https://doi.org/10.1007/JHEP05(2023)160
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DOI: https://doi.org/10.1007/JHEP05(2023)160