Abstract
We study the dS/CFT duality between minimal type-A higher-spin gravity and the free Sp(2N) vector model. We consider the bulk spacetime as “elliptic” de Sitter space dS4/ℤ2, in which antipodal points have been identified. We apply a technique from arXiv:1509.05890, which extracts the quantum-mechanical commutators (or Poisson brackets) of the linearized bulk theory in an observable patch of dS4/ℤ2 directly from the boundary 2-point function. Thus, we construct the Lorentzian commutators of the linearized bulk theory from the Euclidean CFT. In the present paper, we execute this technique for the entire higher-spin multiplet, using a higher-spin-covariant language, which provides a promising framework for the future inclusion of bulk interactions. Aside from its importance for dS/CFT, our construction of a Hamiltonian structure for a bulk causal region should be of interest within higher-spin theory itself. The price we pay is a partial symmetry breaking, from the full dS group (and its higher-spin extension) to the symmetry group of an observable patch. While the boundary field theory plays a role in our arguments, the results can be fully expressed within a boundary particle mechanics. Bulk fields arise from this boundary mechanics via a version of second quantization.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.A. Vasiliev, Higher spin gauge theories in four-dimensions, three-dimensions and two-dimensions, Int. J. Mod. Phys. D 5 (1996) 763 [hep-th/9611024] [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories: Star product and AdS space, hep-th/9910096 [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [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].
D. Anninos, T. Hartman and A. Strominger, Higher Spin Realization of the dS/CFT Correspondence, Class. Quant. Grav. 34 (2017) 015009 [arXiv:1108.5735] [INSPIRE].
J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
D. Anninos, F. Denef, R. Monten and Z. Sun, Higher Spin de Sitter Hilbert Space, arXiv:1711.10037 [INSPIRE].
I.F. Halpern and Y. Neiman, Holography and quantum states in elliptic de Sitter space, JHEP 12 (2015) 057 [arXiv:1509.05890] [INSPIRE].
M.K. Parikh, I. Savonije and E.P. Verlinde, Elliptic de Sitter space: dS/Z(2), Phys. Rev. D 67 (2003) 064005 [hep-th/0209120] [INSPIRE].
A. Folacci and N.G. Sanchez, Quantum Field Theory and the ‘Elliptic Interpretation’ of de Sitter Space-time, Nucl. Phys. B 294 (1987) 1111 [INSPIRE].
R. de Mello Koch, A. Jevicki, K. Jin and J.P. Rodrigues, AdS 4 /CF T 3 Construction from Collective Fields, Phys. Rev. D 83 (2011) 025006 [arXiv:1008.0633] [INSPIRE].
D. Das, S.R. Das, A. Jevicki and Q. Ye, Bi-local Construction of Sp(2N)/dS Higher Spin Correspondence, JHEP 01 (2013) 107 [arXiv:1205.5776] [INSPIRE].
R. de Mello Koch, A. Jevicki, J.P. Rodrigues and J. Yoon, Canonical Formulation of O(N) Vector/Higher Spin Correspondence, J. Phys. A 48 (2015) 105403 [arXiv:1408.4800] [INSPIRE].
S.R. Das and A. Jevicki, Large N collective fields and holography, Phys. Rev. D 68 (2003) 044011 [hep-th/0304093] [INSPIRE].
M.A. Vasiliev, Holography, Unfolding and Higher-Spin Theory, J. Phys. A 46 (2013) 214013 [arXiv:1203.5554] [INSPIRE].
O.A. Gelfond and M.A. Vasiliev, Higher Spin Fields in Siegel Space, Currents and Theta Functions, JHEP 03 (2009) 125 [arXiv:0801.2191] [INSPIRE].
D. Anninos, S.A. Hartnoll and D.M. Hofman, Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline, Class. Quant. Grav. 29 (2012) 075002 [arXiv:1109.4942] [INSPIRE].
Y. Neiman, The holographic dual of the Penrose transform, JHEP 01 (2018) 100 [arXiv:1709.08050] [INSPIRE].
L. Hackl and Y. Neiman, Horizon complementarity in elliptic de Sitter space, Phys. Rev. D 91 (2015) 044016 [arXiv:1409.6753] [INSPIRE].
O.A. Gelfond and M.A. Vasiliev, Operator algebra of free conformal currents via twistors, Nucl. Phys. B 876 (2013) 871 [arXiv:1301.3123] [INSPIRE].
R. Penrose and W. Rindler, Spinors And Space-time. Vol. 2: Spinor And Twistor Methods In Space-time Geometry, Cambridge University Press, Cambridge, U.K. (1986) [INSPIRE].
R.S. Ward and R.O. Wells, Twistor geometry and field theory, Cambridge University Press, Cambridge, U.K. (1990) [INSPIRE].
W.B. Case, Wigner functions and Weyl transforms for pedestrians, Am. J. Phys. 76 (2008) 937.
Y. Neiman, Antipodally symmetric gauge fields and higher-spin gravity in de Sitter space, JHEP 10 (2014) 153 [arXiv:1406.3291] [INSPIRE].
G.S. Ng and A. Strominger, State/Operator Correspondence in Higher-Spin dS/CFT, Class. Quant. Grav. 30 (2013) 104002 [arXiv:1204.1057] [INSPIRE].
D. Harlow and D. Stanford, Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].
J.B. Hartle and S.W. Hawking, Wave Function of the Universe, Phys. Rev. D 28 (1983) 2960 [INSPIRE].
Y. Neiman, Twistors and antipodes in de Sitter space, Phys. Rev. D 89 (2014) 063521 [arXiv:1312.7842] [INSPIRE].
V.E. Didenko and M.A. Vasiliev, Static BPS black hole in 4d higher-spin gauge theory, Phys. Lett. B 682 (2009) 305 [Erratum ibid. B 722 (2013) 389] [arXiv:0906.3898] [INSPIRE].
K. Pilch, P. van Nieuwenhuizen and M.F. Sohnius, de Sitter Superalgebras and Supergravity, Commun. Math. Phys. 98 (1985) 105 [INSPIRE].
D. Anninos, F. Denef and D. Harlow, Wave function of Vasiliev’s universe: A few slices thereof, Phys. Rev. D 88 (2013) 084049 [arXiv:1207.5517] [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: 1809.07270
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Neiman, Y. Holographic quantization of linearized higher-spin gravity in the de Sitter causal patch. J. High Energ. Phys. 2018, 33 (2018). https://doi.org/10.1007/JHEP11(2018)033
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2018)033