Duality in the Sachdev-Ye-Kitaev model

Sumit R. Das; Animik Ghosh; Antal Jevicki; Kenta Suzuki

doi:10.1007/978-981-13-2179-5_4

Duality in the Sachdev-Ye-Kitaev model

Sumit R. Das, Animik Ghosh, Antal Jevicki, Kenta Suzuki

Physics And Astronomy

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

In this article, starting from a review of basic aspects of the Sachdev-Ye-Kitaev (SYK) model in the large N limit, we discuss at non-linear-level the deduction of the zero mode effective Schwarzian action, featuring emergent finite reparametrization symmetry. We then discuss the question of identifying the bulk space-time of the SYK model. We explain the need for non-local (Radon-type) transformations on external legs of n-point Green’s functions, leading to a dual theory with Euclidean AdS signature with additional leg-factors. We show that the SYK spectrum and the bi-local propagator can be obtained from a Horava-Witten type compactification of a three dimensional model.

Original language	English
Title of host publication	Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2 - QTS-X/LT-XII, 2017
Editors	Vladimir Dobrev
Pages	43-61
Number of pages	19
DOIs	https://doi.org/10.1007/978-981-13-2179-5_4
State	Published - 2018
Event	International Symposium on Quantum Theory and Symmetries, QTS-X and XII 2017 and International Workshop on Lie Theory and Its Applications in Physics, LT-XII 2017 - Varna, Bulgaria Duration: Jun 19 2017 → Jun 25 2017

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	255
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Symposium on Quantum Theory and Symmetries, QTS-X and XII 2017 and International Workshop on Lie Theory and Its Applications in Physics, LT-XII 2017
Country/Territory	Bulgaria
City	Varna
Period	6/19/17 → 6/25/17

Bibliographical note

Funding Information:
Acknowledgements S.R.D. and A.J. thank the organizers of QTS10 for organizing a very stimulating meeting. We acknowledge helpful discussions with Robert de Melo Koch, Alexei Kitaev, Juan Maldacena, Gautam Mandal, Cheng Peng and Edward Witten on the topics of this work. We also thank Junggi Yoon for collaborations. This work of A.J. and K.S. are supported by the Department of Energy under contract DE-SC0010010. The work of KS is also supported by the Galkin Fellowship Award at Brown University. The work of S.R.D and A.G is partially supported by the National Science Foundation grant NSF-PHY-1521045.

Publisher Copyright:
© Springer Nature Singapore Pte Ltd. 2018.

Keywords

Collective field theory
Holographic correspondence
Large N expansion

ASJC Scopus subject areas

Mathematics (all)

Access to Document

10.1007/978-981-13-2179-5_4

Cite this

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title = "Duality in the Sachdev-Ye-Kitaev model",

abstract = "In this article, starting from a review of basic aspects of the Sachdev-Ye-Kitaev (SYK) model in the large N limit, we discuss at non-linear-level the deduction of the zero mode effective Schwarzian action, featuring emergent finite reparametrization symmetry. We then discuss the question of identifying the bulk space-time of the SYK model. We explain the need for non-local (Radon-type) transformations on external legs of n-point Green{\textquoteright}s functions, leading to a dual theory with Euclidean AdS signature with additional leg-factors. We show that the SYK spectrum and the bi-local propagator can be obtained from a Horava-Witten type compactification of a three dimensional model.",

keywords = "Collective field theory, Holographic correspondence, Large N expansion",

author = "Das, {Sumit R.} and Animik Ghosh and Antal Jevicki and Kenta Suzuki",

note = "Funding Information: Acknowledgements S.R.D. and A.J. thank the organizers of QTS10 for organizing a very stimulating meeting. We acknowledge helpful discussions with Robert de Melo Koch, Alexei Kitaev, Juan Maldacena, Gautam Mandal, Cheng Peng and Edward Witten on the topics of this work. We also thank Junggi Yoon for collaborations. This work of A.J. and K.S. are supported by the Department of Energy under contract DE-SC0010010. The work of KS is also supported by the Galkin Fellowship Award at Brown University. The work of S.R.D and A.G is partially supported by the National Science Foundation grant NSF-PHY-1521045. Publisher Copyright: {\textcopyright} Springer Nature Singapore Pte Ltd. 2018.; International Symposium on Quantum Theory and Symmetries, QTS-X and XII 2017 and International Workshop on Lie Theory and Its Applications in Physics, LT-XII 2017 ; Conference date: 19-06-2017 Through 25-06-2017",

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doi = "10.1007/978-981-13-2179-5_4",

language = "English",

isbn = "9789811321788",

series = "Springer Proceedings in Mathematics and Statistics",

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editor = "Vladimir Dobrev",

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Das, SR, Ghosh, A, Jevicki, A & Suzuki, K 2018, Duality in the Sachdev-Ye-Kitaev model. in V Dobrev (ed.), Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2 - QTS-X/LT-XII, 2017. Springer Proceedings in Mathematics and Statistics, vol. 255, pp. 43-61, International Symposium on Quantum Theory and Symmetries, QTS-X and XII 2017 and International Workshop on Lie Theory and Its Applications in Physics, LT-XII 2017, Varna, Bulgaria, 6/19/17. https://doi.org/10.1007/978-981-13-2179-5_4

Duality in the Sachdev-Ye-Kitaev model. / Das, Sumit R.; Ghosh, Animik; Jevicki, Antal et al.
Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2 - QTS-X/LT-XII, 2017. ed. / Vladimir Dobrev. 2018. p. 43-61 (Springer Proceedings in Mathematics and Statistics; Vol. 255).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N1 - Funding Information: Acknowledgements S.R.D. and A.J. thank the organizers of QTS10 for organizing a very stimulating meeting. We acknowledge helpful discussions with Robert de Melo Koch, Alexei Kitaev, Juan Maldacena, Gautam Mandal, Cheng Peng and Edward Witten on the topics of this work. We also thank Junggi Yoon for collaborations. This work of A.J. and K.S. are supported by the Department of Energy under contract DE-SC0010010. The work of KS is also supported by the Galkin Fellowship Award at Brown University. The work of S.R.D and A.G is partially supported by the National Science Foundation grant NSF-PHY-1521045. Publisher Copyright: © Springer Nature Singapore Pte Ltd. 2018.

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N2 - In this article, starting from a review of basic aspects of the Sachdev-Ye-Kitaev (SYK) model in the large N limit, we discuss at non-linear-level the deduction of the zero mode effective Schwarzian action, featuring emergent finite reparametrization symmetry. We then discuss the question of identifying the bulk space-time of the SYK model. We explain the need for non-local (Radon-type) transformations on external legs of n-point Green’s functions, leading to a dual theory with Euclidean AdS signature with additional leg-factors. We show that the SYK spectrum and the bi-local propagator can be obtained from a Horava-Witten type compactification of a three dimensional model.

AB - In this article, starting from a review of basic aspects of the Sachdev-Ye-Kitaev (SYK) model in the large N limit, we discuss at non-linear-level the deduction of the zero mode effective Schwarzian action, featuring emergent finite reparametrization symmetry. We then discuss the question of identifying the bulk space-time of the SYK model. We explain the need for non-local (Radon-type) transformations on external legs of n-point Green’s functions, leading to a dual theory with Euclidean AdS signature with additional leg-factors. We show that the SYK spectrum and the bi-local propagator can be obtained from a Horava-Witten type compactification of a three dimensional model.

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BT - Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2 - QTS-X/LT-XII, 2017

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Duality in the Sachdev-Ye-Kitaev model

Abstract

Publication series

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Bibliographical note

Keywords

ASJC Scopus subject areas

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