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Multipartite edge modes and tensor networks
by Chris Akers, Ronak M Soni and Annie Y. Wei
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Ronak Soni |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202406_00063v2 (pdf) |
| Date accepted: | 2024-10-23 |
| Date submitted: | 2024-09-25 06:39 |
| Submitted by: | Soni, Ronak |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Holographic tensor networks model AdS/CFT, but so far they have been limited by involving only systems that are very different from gravity. Unfortunately, we cannot straightforwardly discretize gravity to incorporate it, because that would break diffeomorphism invariance. In this note, we explore a resolution. In low dimensions gravity can be written as a topological gauge theory, which can be discretized without breaking gauge-invariance. However, new problems arise. Foremost, we now need a qualitatively new kind of "area operator," which has no relation to the number of links along the cut and is instead topological. Secondly, the inclusion of matter becomes trickier. We successfully construct a tensor network both including matter and with this new type of area. Notably, while this area is still related to the entanglement in "edge mode" degrees of freedom, the edge modes are no longer bipartite entangled pairs. Instead they are highly multipartite. Along the way, we calculate the entropy of novel subalgebras in a particular topological gauge theory. We also show that the multipartite nature of the edge modes gives rise to non-commuting area operators, a property that other tensor networks do not exhibit.
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. Core 7, 070 (2024)
Reports on this Submission
Report #3 by Anonymous (Referee 1) on 2024-10-15 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202406_00063v2, delivered 2024-10-15, doi: 10.21468/SciPost.Report.9925
Report
The authors have made several clarifications and improvements to the paper.
One issue remains unresolved and continues to be a concern: these proposals are based on expectations of a finite rank discrete gauge group, and where no large N limit has to be taken. Therefore, it is still unclear to us why we can take the area term/topological term ratio very seriously as a "problem" to solve. While the reply explains that the boundary is not expected to be gapped, and that some operators in the bulk (the central operator) carries an interpretation in the boundary CFT, that is a very weak reference of the boundary CFT -- for example boundary conditions do not play any role in this computation. The factorization map also seems indifferent to the precise boundary conditions.
Even comparing with the usual semi-classical AdS/CFT, this is odd because the asymptotic boundary conditions do make a huge difference to the computation, without which everything changes, including the Brown-Henneaux asymptotic symmetries of the boundary theory.
Inspecting the wave-function, it is unclear how this tensor network would not describing a gapped state at the boundary rather than a CFT. If we can not be certain of a difference (for example seeing the c/3 log L term showing up), then can we really be certain that the entanglement entropy is given by the gapped bulk alone? The discussion at the end of section 5/ or near equation 4.2 do not seem to resolve this tension or justify why we do not need to worry about the CFT more, or take more care in the large N limit. Without clear justification and reasoning, we find the factorization map overly ad hoc and lacking sufficient grounding to be considered physically meaningful.
For these reasons, while we acknowledge that there is a proposal based on the factorization map that resolves some issues that might be there, it remains inconclusive whether these are real issues, and to what extent the modified tensor network carries more resemblance to a CFT ground state.
Nevertheless, we appreciate the clarifications and improvements, and we defer a decision to the editor.
Recommendation
Reject