Abstract
We discuss the algebra of operators in AdS-Rindler wedge, particularly in AdS5/CFT4. We explicitly construct the algebra at N = ∞ limit and discuss its Type III1 nature. We will consider 1/N corrections to the theory and using a novel way of renormalizing the area of Ryu-Takayanagi surface, describe how several divergences can be renormalized and the algebra becomes Type II∞. This will make it possible to associate a density matrix to any state in the Hilbert space and thus a von Neumann entropy.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Leutheusser and H. Liu, Emergent times in holographic duality, arXiv:2112.12156 [INSPIRE].
S. Leutheusser and H. Liu, Causal connectability between quantum systems and the black hole interior in holographic duality, arXiv:2110.05497 [INSPIRE].
E. Witten, Gravity and the crossed product, JHEP 10 (2022) 008 [arXiv:2112.12828] [INSPIRE].
V. Chandrasekaran, R. Longo, G. Penington and E. Witten, An algebra of observables for de Sitter space, JHEP 02 (2023) 082 [arXiv:2206.10780] [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT: A boundary view of horizons and locality, Phys. Rev. D 73 (2006) 086003 [hep-th/0506118] [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Holographic representation of local bulk operators, Phys. Rev. D 74 (2006) 066009 [hep-th/0606141] [INSPIRE].
A. Almheiri, X. Dong and D. Harlow, Bulk Locality and Quantum Error Correction in AdS/CFT, JHEP 04 (2015) 163 [arXiv:1411.7041] [INSPIRE].
R. Haag, Local quantum physics: Fields, particles, algebras, Springer (1992) [INSPIRE].
R.F. Streater and A.S. Wightman, PCT, spin and statistics, and all that, <bbl:err:publisher> (1989) [INSPIRE].
J. von Neumann, On Rings of Operators. Reduction Theory, Annals Math. 50 (1949) 401.
J. von Neumann, On Rings of Operators. III, Annals Math. 41 (1940) 94.
T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
D. Harlow and D. Stanford, Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].
G. Festuccia and H. Liu, The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories, JHEP 12 (2007) 027 [hep-th/0611098] [INSPIRE].
E. Verlinde and K.M. Zurek, Spacetime Fluctuations in AdS/CFT, JHEP 04 (2020) 209 [arXiv:1911.02018] [INSPIRE].
M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
K. Krasnov and J.-M. Schlenker, On the renormalized volume of hyperbolic 3-manifolds, Commun. Math. Phys. 279 (2008) 637 [math/0607081] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
Acknowledgments
I would like to thank Kyriakos Papadodimas for the useful discussions and a careful reading of the article. I also want to thank the CERN-TH for their hospitality during the preparation of this paper. The research is partially supported by INFN Iniziativa Specifica String Theory and Fundamental Interactions.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2208.04258
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Bahiru, E. Algebra of operators in an AdS-Rindler wedge. J. High Energ. Phys. 2023, 197 (2023). https://doi.org/10.1007/JHEP06(2023)197
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2023)197