Abstract
According to static patch holography, de Sitter space admits a unitary quantum description in terms of a dual theory living on the stretched horizon, that is a timelike surface close to the cosmological horizon. In this manuscript, we compute several holographic complexity conjectures in a periodic extension of the Schwarzschild-de Sitter black hole. We consider multiple configurations of the stretched horizons to which geometric objects are anchored. The holographic complexity proposals admit a hyperfast growth when the gravitational observables only lie in the cosmological patch, except for a class of complexity=anything observables that admit a linear growth. All the complexity conjectures present a linear increase when restricted to the black hole patch, similar to the AdS case. When both the black hole and the cosmological regions are probed, codimension-zero proposals are time-independent, while codimension-one proposals can have non-trivial evolution with linear increase at late times. As a byproduct of our analysis, we find that codimension-one spacelike surfaces are highly constrained in Schwarzschild-de Sitter space. Therefore, different locations of the stretched horizon give rise to different behaviours of the complexity conjectures.
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Acknowledgments
We thank Victor Franken, Thomas Hertog, Rob Myers, and Shan-Ming Ruan for useful discussions, and especially Rotem Berman and Juan Pedraza for their initial collaboration and interesting comments. We thank Roberto Auzzi, Shira Chapman and Giuseppe Nardelli for useful comments and discussions on a preliminary version of this work. We benefited from the workshop “Gravity meets quantum information” in Wurzburg, which allowed this collaboration to start. SEAG thanks the IFT-UAM/CSIC, the University of Amsterdam, the Delta Institute for Theoretical Physics, and the International Centre for Theoretical Physics for their hospitality and financial support during several phases of the project, and the Research Foundation - Flanders (FWO) for also providing mobility support. The work of SEAG is partially supported by the FWO Research Project G0H9318N and the inter-university project iBOF/21/084. The work of SB is supported by the Israel Science Foundation (grant No. 1417/21), the German Research Foundation through a German-Israeli Project Cooperation (DIP) grant “Holography and the Swampland”, Carole and Marcus Weinstein through the BGU Presidential Faculty Recruitment Fund, and the ISF Center of Excellence for theoretical high energy physics. SB is also supported by an Azrieli fellowship awarded by the Azrieli foundation. The work of NZ is supported by MEXT KAKENHI Grant-in-Aid for Transformative Research Areas A “Extreme Universe” No. 21H05184.
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Aguilar-Gutierrez, S.E., Baiguera, S. & Zenoni, N. Holographic complexity of the extended Schwarzschild-de Sitter space. J. High Energ. Phys. 2024, 201 (2024). https://doi.org/10.1007/JHEP05(2024)201
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DOI: https://doi.org/10.1007/JHEP05(2024)201