Three dimensional view of arbitrary q SYK models

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

doi:10.1007/JHEP02(2018)162

Three dimensional view of arbitrary q SYK models

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

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

Abstract

In [15] it was shown that the spectrum and bilocal propagator of SYK model with four fermion interactions can be realized as a three dimensional model in AdS₂ ×S¹/Z₂ with nontrivial boundary conditions in the additional dimension. In this paper we show that a similar picture holds for generalizations of the SYK model with q-fermion interactions. The 3D realization is now given on a space whose metric is conformal to AdS₂ × S¹/Z₂ and is subject to a non-trivial potential in addition to a delta function at the center of the interval. It is shown that a Horava-Witten compactification reproduces the exact SYK spectrum and a non-standard propagator between points which lie at the center of the interval exactly agrees with the bilocal propagator. As q → ∞, the wave function of one of the modes at the center of the interval vanish as 1/q, while the others vanish as 1/q², in a way consistent with the fact that in the SYK model only one of the modes contributes to the bilocal propagator in this limit.

Original language	English
Article number	162
Journal	Journal of High Energy Physics
Volume	2018
Issue number	2
DOIs	https://doi.org/10.1007/JHEP02(2018)162
State	Published - Feb 1 2018

Bibliographical note

Publisher Copyright:
© 2018, The Author(s).

Funding

We thank Juan Maldacena and Pranjal Nayak for discussions, and Ed Witten for a correspondence. This work of AJ and KS is 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 SRD and AG is partially supported by the National Science Foundation grant NSF-PHY-1521045. S.R.D. would like to thank Yukawa Institute for Theoretical Physics, Kyoto University and Tata Institute of Fundamental Research, Mumbai for hospitality during the completion of this work. AG would like to thank the lecturers and participants of the TASI 2017 program, and the University of Colorado, Boulder for hospitality during the completion of this work.

Funders	Funder number
National Science Foundation Arctic Social Science Program	1521045, NSF-PHY-1521045
U.S. Department of Energy EPSCoR	DE-SC0010010
Brown University

Keywords

1/N Expansion
2D Gravity
AdS-CFT Correspondence
Gauge-gravity correspondence

ASJC Scopus subject areas

Nuclear and High Energy Physics

Access to Document

10.1007/JHEP02(2018)162

Cite this

@article{7c819b30bc304b4eadd9d63c880d1185,

title = "Three dimensional view of arbitrary q SYK models",

abstract = "In [15] it was shown that the spectrum and bilocal propagator of SYK model with four fermion interactions can be realized as a three dimensional model in AdS2 ×S1/Z2 with nontrivial boundary conditions in the additional dimension. In this paper we show that a similar picture holds for generalizations of the SYK model with q-fermion interactions. The 3D realization is now given on a space whose metric is conformal to AdS2 × S1/Z2 and is subject to a non-trivial potential in addition to a delta function at the center of the interval. It is shown that a Horava-Witten compactification reproduces the exact SYK spectrum and a non-standard propagator between points which lie at the center of the interval exactly agrees with the bilocal propagator. As q → ∞, the wave function of one of the modes at the center of the interval vanish as 1/q, while the others vanish as 1/q2, in a way consistent with the fact that in the SYK model only one of the modes contributes to the bilocal propagator in this limit.",

keywords = "1/N Expansion, 2D Gravity, AdS-CFT Correspondence, Gauge-gravity correspondence",

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

note = "Publisher Copyright: {\textcopyright} 2018, The Author(s).",

year = "2018",

month = feb,

day = "1",

doi = "10.1007/JHEP02(2018)162",

language = "English",

volume = "2018",

number = "2",

}

TY - JOUR

T1 - Three dimensional view of arbitrary q SYK models

AU - Das, Sumit R.

AU - Ghosh, Animik

AU - Jevicki, Antal

AU - Suzuki, Kenta

PY - 2018/2/1

Y1 - 2018/2/1

N2 - In [15] it was shown that the spectrum and bilocal propagator of SYK model with four fermion interactions can be realized as a three dimensional model in AdS2 ×S1/Z2 with nontrivial boundary conditions in the additional dimension. In this paper we show that a similar picture holds for generalizations of the SYK model with q-fermion interactions. The 3D realization is now given on a space whose metric is conformal to AdS2 × S1/Z2 and is subject to a non-trivial potential in addition to a delta function at the center of the interval. It is shown that a Horava-Witten compactification reproduces the exact SYK spectrum and a non-standard propagator between points which lie at the center of the interval exactly agrees with the bilocal propagator. As q → ∞, the wave function of one of the modes at the center of the interval vanish as 1/q, while the others vanish as 1/q2, in a way consistent with the fact that in the SYK model only one of the modes contributes to the bilocal propagator in this limit.

AB - In [15] it was shown that the spectrum and bilocal propagator of SYK model with four fermion interactions can be realized as a three dimensional model in AdS2 ×S1/Z2 with nontrivial boundary conditions in the additional dimension. In this paper we show that a similar picture holds for generalizations of the SYK model with q-fermion interactions. The 3D realization is now given on a space whose metric is conformal to AdS2 × S1/Z2 and is subject to a non-trivial potential in addition to a delta function at the center of the interval. It is shown that a Horava-Witten compactification reproduces the exact SYK spectrum and a non-standard propagator between points which lie at the center of the interval exactly agrees with the bilocal propagator. As q → ∞, the wave function of one of the modes at the center of the interval vanish as 1/q, while the others vanish as 1/q2, in a way consistent with the fact that in the SYK model only one of the modes contributes to the bilocal propagator in this limit.

KW - 1/N Expansion

KW - 2D Gravity

KW - AdS-CFT Correspondence

KW - Gauge-gravity correspondence

UR - http://www.scopus.com/inward/record.url?scp=85042762451&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042762451&partnerID=8YFLogxK

U2 - 10.1007/JHEP02(2018)162

DO - 10.1007/JHEP02(2018)162

M3 - Article

AN - SCOPUS:85042762451

SN - 1126-6708

VL - 2018

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 2

M1 - 162

ER -

Three dimensional view of arbitrary q SYK models

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this