Abstract
This letter explores a transition in the type of von Neumann algebra for asymptotically AdS spacetimes from the implementations of the different gravitational constraints. We denote it as the centaur-algebra of observables. In the first part of the letter, we employ a class of flow geometries interpolating between AdS2 and dS2 spaces, the centaur geometries. We study the type II∞ crossed product algebra describing the semiclassical gravitational theory, and we explore the algebra of bounded sub-regions in the bulk theory following \( T\overline{T} \) deformations of the geometry and study the gravitational constraints with respect to the quasi-local Brown-York energy of the system at a finite cutoff. In the second part, we study arbitrary asymptotically AdS spacetimes, where we implement the boundary protocol of an infalling observer modeled as a probe black hole proposed by [1] to study modifications in the algebra. In both situations, we show how incorporating the constraints requires a type II1 description.
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Acknowledgments
We would like to thank Shadi Ali Ahmad, Dio Anninos, Damián Galante, Stefan Hollands, Ro Jefferson, Andrew Rolph, Sirui Shuai, Andrew Svesko, Eleanor Harris, and Yixu Wang for useful discussions on centaur spacetimes and von Neumann algebras, and specially Manus Visser for early collaboration. 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. EB also wants to thank the CERN-TH for their hospitality during the preparation of this paper. The work of SEAG is partially supported by the KU Leuven C1 grant ZKD1118 C16/16/005. The work of EB is partially supported by the Eramsus+ Trainee-ship programme and the INFN Iniziativa Specifica String Theory and Fundamental Interactions. RE is supported by the Dushi Zhuanxiang Fellowship and acknowledges a Shuimu Scholarship as part of the “Shuimu Tsinghua Scholar” Program.
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Aguilar-Gutierrez, S.E., Bahiru, E. & Espíndola, R. The centaur-algebra of observables. J. High Energ. Phys. 2024, 8 (2024). https://doi.org/10.1007/JHEP03(2024)008
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DOI: https://doi.org/10.1007/JHEP03(2024)008