Size of bulk fermions in the SYK model
- Creators
- Lensky, Yuri D.
- Qi, Xiao-Liang
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Zhang, Pengfei
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.
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).Attached Files
Published - Lensky2020_Article_SizeOfBulkFermionsInTheSYKMode.pdf
Submitted - 2002.01961.pdf
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Additional details
- Eprint ID
- 105985
- Resolver ID
- CaltechAUTHORS:20201012-132120667
- NSF
- PHY-1720504
- Fannie and John Hertz Foundation
- Walter Burke Institute for Theoretical Physics, Caltech
- Department of Energy (DOE)
- DE-SC0019380
- Created
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2020-10-12Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics