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Title: Three dimensional view of arbitrary q SYK models

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 AdS 2 ×S 1/Z 2 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 AdS 2 × S 1/Z 2 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/q 2, 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.
Authors:
 [1] ;  [1] ;  [2] ;  [2]
  1. Univ. of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy
  2. Brown Univ., Providence, RI (United States). Dept. of Physics
Publication Date:
Grant/Contract Number:
SC0010010
Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 2; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Research Org:
Brown Univ., Providence, RI (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdS-CFT Correspondence; Gauge-gravity correspondence; 2D Gravity; 1/N Expansion
OSTI Identifier:
1502069

Das, Sumit R., Ghosh, Animik, Jevicki, Antal, and Suzuki, Kenta. Three dimensional view of arbitrary q SYK models. United States: N. p., Web. doi:10.1007/jhep02(2018)162.
Das, Sumit R., Ghosh, Animik, Jevicki, Antal, & Suzuki, Kenta. Three dimensional view of arbitrary q SYK models. United States. doi:10.1007/jhep02(2018)162.
Das, Sumit R., Ghosh, Animik, Jevicki, Antal, and Suzuki, Kenta. 2018. "Three dimensional view of arbitrary q SYK models". United States. doi:10.1007/jhep02(2018)162. https://www.osti.gov/servlets/purl/1502069.
@article{osti_1502069,
title = {Three dimensional view of arbitrary q SYK models},
author = {Das, Sumit R. and Ghosh, Animik and Jevicki, Antal and Suzuki, Kenta},
abstractNote = {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.},
doi = {10.1007/jhep02(2018)162},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2018,
place = {United States},
year = {2018},
month = {2}
}