Abstract
Built on our observation that entangling surfaces of the boundary field theory are great co-dimension one spheres in the context of DS/dS correspondence, we study some information theoretic quantities of the field theory dual intensively using holographic proposals. We will focus on entanglement entropy (EE), entanglement of purification (EoP) and complexity. Several fundamental observations and analysis are provided. For EE, we focus on its scaling behavior, which indicates the nature of the relevant degrees of freedom. Moreover, we find that EE provides us with important information of the energy spectrum in pure dS and it also leads us to the speculation that the field theory dual is chaotic or non-integrable. For EoP, an interesting phenomenon we call “Entanglement Wedge Cross Section (EWCS) Jump” is observed according to which we propose two puzzles regarding EoP and EE in the context of dS holography. For complexity, we find that the Complexity=Volume proposal does not provide a well-defined way to compute complexity for pure dS. However, it does provide a well-defined way to compute complexity in the \( T\overline{T} \) + Λ2 deformed case. At the end, we will use the surface/state correspondence to resolve all the puzzles and hence reach a consistent information theoretic picture of dS holography. Moreover, we will provide evidence for our former proposal that the \( T\overline{T} \) + ⋯ deformations are operating quantum circuits and study the non-locality of the field theory algebra suggested by the surface/state correspondence.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Karch, Autolocalization in de Sitter space, JHEP 07 (2003) 050 [hep-th/0305192] [INSPIRE].
L. Randall and R. Sundrum, An Alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].
M. Alishahiha, A. Karch, E. Silverstein and D. Tong, The dS/dS correspondence, AIP Conf. Proc. 743 (2004) 393 [hep-th/0407125] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
A. Lewkowycz, J. Liu, E. Silverstein and G. Torroba, \( T\overline{T} \) and EE, with implications for (A)dS subregion encodings, arXiv:1909.13808 [INSPIRE].
X. Dong, E. Silverstein and G. Torroba, de Sitter Holography and Entanglement Entropy, JHEP 07 (2018) 050 [arXiv:1804.08623] [INSPIRE].
H. Geng, S. Grieninger and A. Karch, Entropy, Entanglement and Swampland Bounds in DS/dS, JHEP 06 (2019) 105 [arXiv:1904.02170] [INSPIRE].
V. Gorbenko, E. Silverstein and G. Torroba, dS/dS and \( T\overline{T} \), JHEP 03 (2019) 085 [arXiv:1811.07965] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \( T\overline{T} \), JHEP 04 (2018) 010 [arXiv:1611.03470] [INSPIRE].
P. Nguyen, T. Devakul, M.G. Halbasch, M.P. Zaletel and B. Swingle, Entanglement of purification: from spin chains to holography, JHEP 01 (2018) 098 [arXiv:1709.07424] [INSPIRE].
T. Takayanagi and K. Umemoto, Entanglement of purification through holographic duality, Nature Phys. 14 (2018) 573 [arXiv:1708.09393] [INSPIRE].
M. Alishahiha, Holographic Complexity, Phys. Rev. D 92 (2015) 126009 [arXiv:1509.06614] [INSPIRE].
M. Miyaji and T. Takayanagi, Surface/State Correspondence as a Generalized Holography, PTEP 2015 (2015) 073B03 [arXiv:1503.03542] [INSPIRE].
H. Geng, \( T\overline{T} \) Deformation and the Complexity=Volume Conjecture, arXiv:1910.08082 [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
C. Arias, F. Diaz, R. Olea and P. Sundell, Liouville description of conical defects in dS4, Gibbons-Hawking entropy as modular entropy and dS3 holography, arXiv:1906.05310 [INSPIRE].
C. Arias, F. Diaz and P. Sundell, de Sitter Space and Entanglement, Class. Quant. Grav. 37 (2020) 015009 [arXiv:1901.04554] [INSPIRE].
S. Grieninger, Entanglement entropy and \( T\overline{T} \) deformations beyond antipodal points from holography, JHEP 11 (2019) 171 [arXiv:1908.10372] [INSPIRE].
D. Harlow, TASI Lectures on the Emergence of Bulk Physics in AdS/CFT, PoS(TASI2017)002 (2018) [arXiv:1802.01040] [INSPIRE].
J. Cardy, \( T\overline{T} \) deformation of correlation functions, JHEP 12 (2019) 160 [arXiv:1907.03394] [INSPIRE].
T. Faulkner and A. Lewkowycz, Bulk locality from modular flow, JHEP 07 (2017) 151 [arXiv:1704.05464] [INSPIRE].
L. D’Alessio, Y. Kafri, A. Polkovnikov and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65 (2016) 239 [arXiv:1509.06411] [INSPIRE].
B.M. Terhal, M. Horodecki, D.W. Leung and D.P. DiVincenzo, The entanglement of purification, J. Math. Phys. 43 (2002) 4286 [quant-ph/0202044].
S. Dutta and T. Faulkner, A canonical purification for the entanglement wedge cross-section, arXiv:1905.00577 [INSPIRE].
J. Kudler-Flam and S. Ryu, Entanglement negativity and minimal entanglement wedge cross sections in holographic theories, Phys. Rev. D 99 (2019) 106014 [arXiv:1808.00446] [INSPIRE].
K. Tamaoka, Entanglement Wedge Cross Section from the Dual Density Matrix, Phys. Rev. Lett. 122 (2019) 141601 [arXiv:1809.09109] [INSPIRE].
L. Susskind, Computational Complexity and Black Hole Horizons, Fortsch. Phys. 64 (2016) 44 [arXiv:1403.5695] [INSPIRE].
R. Horodecki, P. Horodecki, M. Horodecki and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81 (2009) 865 [quant-ph/0702225] [INSPIRE].
E. Witten, APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum field theory, Rev. Mod. Phys. 90 (2018) 045003 [arXiv:1803.04993] [INSPIRE].
H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter Conjectures on the Swampland, Phys. Lett. B 788 (2019) 180 [arXiv:1810.05506] [INSPIRE].
J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge University Press (2007) [INSPIRE].
C.V. Johnson, D-branes, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2005) [INSPIRE].
H. Geng, Distance Conjecture and De-Sitter Quantum Gravity, arXiv:1910.03594 [INSPIRE].
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
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1911.02644
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
Geng, H. Some information theoretic aspects of de-Sitter holography. J. High Energ. Phys. 2020, 5 (2020). https://doi.org/10.1007/JHEP02(2020)005
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2020)005