Lensky, Yuri D. and Qi, Xiao-Liang and Zhang, Pengfei (2020) Size of bulk fermions in the SYK model. Journal of High Energy Physics, 2020 (10). Art. No. 53. ISSN 1029-8479. doi:10.1007/jhep10(2020)053. https://resolver.caltech.edu/CaltechAUTHORS:20201012-132120667
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Abstract
The study of quantum gravity in the form of the holographic duality has uncovered and motivated the detailed investigation of various diagnostics of quantum chaos. One such measure is the operator size distribution, which characterizes the size of the support region of an operator and its evolution under Heisenberg evolution. In this work, we examine the role of the operator size distribution in holographic duality for the Sachdev-Ye-Kitaev (SYK) model. Using an explicit construction of AdS₂ bulk fermion operators in a putative dual of the low temperature SYK model, we study the operator size distribution of the boundary and bulk fermions. Our result provides a direct derivation of the relationship between (effective) operator size of both the boundary and bulk fermions and bulk SL(2; ℝ) generators.
| Item Type: | Article | ||||||||||
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| Additional Information: | © 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: April 15, 2020; Revised: August 14, 2020; Accepted: September 5, 2020; Published: October 8, 2020. We would like to thank Yingfei Gu, Henry Lin, Douglas Stanford, Zhuo-Yu Xian and Ying Zhao for helpful discussion, as well as the anonymous JHEP reviewer for insightful comments. PZ would like to thank Yingfei Gu for bring his attention to the operator size of SYK models in the low temperature limit. This work is supported by the National Science Foundation Grant No. 1720504 (YL and XLQ), the Hertz Foundation (YL) and the Walter Burke Institute for Theoretical Physics at Caltech (PZ). This work is also supported in part by the DOE Office of Science, Office of High Energy Physics, the grant DE-SC0019380 (XLQ). | ||||||||||
| Group: | Walter Burke Institute for Theoretical Physics | ||||||||||
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| Subject Keywords: | AdS-CFT Correspondence; Space-Time Symmetries; 2D Gravity; Models of Quantum Gravity | ||||||||||
| Issue or Number: | 10 | ||||||||||
| DOI: | 10.1007/jhep10(2020)053 | ||||||||||
| Record Number: | CaltechAUTHORS:20201012-132120667 | ||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20201012-132120667 | ||||||||||
| Official Citation: | Lensky, Y.D., Qi, X. & Zhang, P. Size of bulk fermions in the SYK model. J. High Energ. Phys. 2020, 53 (2020). https://doi.org/10.1007/JHEP10(2020)053 | ||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||
| ID Code: | 105985 | ||||||||||
| Collection: | CaltechAUTHORS | ||||||||||
| Deposited By: | Tony Diaz | ||||||||||
| Deposited On: | 12 Oct 2020 20:34 | ||||||||||
| Last Modified: | 16 Nov 2021 18:48 |
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