We show that the spectrum of the SYK model can be interpreted as that of a 3D scalar coupled to gravity. The scalar has a mass which is at the Breitenholer-Freedman bound of AdS2, and subject to a delta function potential at the center of the interval along the third direction. This., through Kaluza-Klein procedure on AdS2 × (S1)/Z2, generates the spectrum reproducing the bi-local propagator at strong coupling. Furthermore., the leading 1/J correction calculated in this picture reproduces the known correction to the poles of the SYK propagator, providing credence to a conjecture that the bulk dual of this model can be interpreted as a three dimensional theory.
|Journal||Journal of High Energy Physics|
|State||Published - Sep 1 2017|
Bibliographical noteFunding Information:
We acknowledge useful conversations with Robert de Melo Koch, Animik Ghosh, Juan Maldacena, Cheng Peng, Al Shapere, Edward Witten and Junggi Yoon on the topics of this paper. We also thank Wenbo Fu, Alexei Kitaev, Grigory Tarnopolsky and Jacobus Verbaarschot for relevant discussions on the SYK model. This work is supported by the Department of Energy under contract DE-SC0010010. The work of SRD is partially supported by the National Science Foundation grant NSF-PHY-1521045. AJ would like to thank the Galileo Galilei Institute for Theoretical Physics (GGI) for the hospitality and INFN for partial support during the completion of this work, within the program “New Developments in AdS3/CFT2 Holography”. We also learned of possibly related work by Marika Taylor .
© 2017, The Author(s).
- 1/N Expansion
- 2D Gravity
- AdS-CFT Correspondence
- Gauge-gravity correspondence
ASJC Scopus subject areas
- Nuclear and High Energy Physics