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Holographic tensor network for double-scaled SYK
by Kazumi Okuyama
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Submission summary
| Authors (as registered SciPost users): | Kazumi Okuyama |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2503.23003v3 (pdf) |
| Date accepted: | Sept. 10, 2025 |
| Date submitted: | Aug. 20, 2025, 3:37 a.m. |
| Submitted by: | Kazumi Okuyama |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We construct a holographic tensor network for the double-scaled SYK model (DSSYK). The moment of the transfer matrix of DSSYK can be mapped to the matrix product state (MPS) of a spin chain. By adding the height direction as a holographic direction, we recast the MPS for DSSYK into the holographic tensor network whose building block is a 4-index tensor with the bond dimension three.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Published as SciPost Phys. 19, 083 (2025)
Reports on this Submission
Report #1 by Anonymous (Referee 2) on 2025-9-6 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2503.23003v3, delivered 2025-09-06, doi: 10.21468/SciPost.Report.11881
Strengths
1-The presentation is clear and pedagogical.
2-Pointed out a novel correspondence of double-scaled SYK model with a tensor network model, and showed how the partition functions and two-point function can be reproduced from the tensor network side.
2-Pointed out a novel correspondence of double-scaled SYK model with a tensor network model, and showed how the partition functions and two-point function can be reproduced from the tensor network side.
Weaknesses
The extent to which this correspondence holds is unclear. See the report for further details.
Report
Regarding Higher-point correlation functions:
It remains unclear whether higher-point functions, particularly those involving nontrivial topologies or crossing configurations, can be fully reproduced within the tensor network framework. Notably, the appearance of the quantum R-matrix in the crossed four-point function, an essential structure known to encode the chaotic dynamics of DSSYK, has not been addressed in this work.
Semi-classical and Schwarzian limit:
While it is established that DSSYK reduces to JT gravity on the Euclidean disk in the Schwarzian regime, it is natural to ask what the corresponding limit is on the tensor network side. Specifically, how does the tensor network encode the Schwarzian dynamics, and what are the signatures of semi-classical gravitational behavior in its structure? A detailed understanding of this limit would not only shed light on the holographic duality in tensor networks but also offer insights into the emergent geometry and dynamics in the low-energy, semi-classical regime.
It remains unclear whether higher-point functions, particularly those involving nontrivial topologies or crossing configurations, can be fully reproduced within the tensor network framework. Notably, the appearance of the quantum R-matrix in the crossed four-point function, an essential structure known to encode the chaotic dynamics of DSSYK, has not been addressed in this work.
Semi-classical and Schwarzian limit:
While it is established that DSSYK reduces to JT gravity on the Euclidean disk in the Schwarzian regime, it is natural to ask what the corresponding limit is on the tensor network side. Specifically, how does the tensor network encode the Schwarzian dynamics, and what are the signatures of semi-classical gravitational behavior in its structure? A detailed understanding of this limit would not only shed light on the holographic duality in tensor networks but also offer insights into the emergent geometry and dynamics in the low-energy, semi-classical regime.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Author: Kazumi Okuyama on 2025-09-07 [id 5792]
(in reply to Report 1 on 2025-09-06)The multi-point functions and the JT gravity limit are beyond the scope of this paper. They are future problems.