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 qfermion 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 nontrivial potential in addition to a delta function at the center of the interval. It is shown that a HoravaWitten compactification reproduces the exact SYK spectrum and a nonstandard 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]}
 Univ. of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy
 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 10298479
 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; AdSCFT Correspondence; Gaugegravity 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 qfermion interactions. The 3D realization is now given on a space whose metric is conformal to AdS2 × S1/Z2 and is subject to a nontrivial potential in addition to a delta function at the center of the interval. It is shown that a HoravaWitten compactification reproduces the exact SYK spectrum and a nonstandard 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}
}