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Thickening and sickening the SYK model
by D. V. Khveshchenko
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Submission summary
| Authors (as registered SciPost users): | Dmitri Khveshchenko |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1705.03956v4 (pdf) |
| Date submitted: | 2018-05-31 02:00 |
| Submitted by: | Khveshchenko, Dmitri |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We discuss higher dimensional generalizations of the 0+1-dimensional Sachdev-Ye-Kitaev (SYK) model that has recently become the focus of intensive interdisciplinary studies by, both, the condensed matter and field-theoretical communities. Unlike the previous constructions where multiple SYK copies would be coupled to each other and/or hybridized with itinerant fermions via spatially short-ranged random hopping processes, we study algebraically varying long-range (spatially and/or temporally) correlated random couplings in the general d+1 dimensions. Such pertinent topics as translationally-invariant strong-coupling solutions, emergent reparametrization symmetry, effective action for fluctuations, chaotic behavior, and diffusive transport (or a lack thereof) are all addressed. We find that the most appealing properties of the original SYK model that suggest the existence of its 1+1-dimensional holographic gravity dual do not survive the aforementioned generalizations, thus lending no additional support to the hypothetical broad (including 'non-AdS/non-CFT') holographic correspondence.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2018-6-13 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1705.03956v4, delivered 2018-06-13, doi: 10.21468/SciPost.Report.499
Report
In the revised version the author answers my questions and implements changes except the last one suggested. I should have been more precise in the request. To me the pre-last paragraph of the manuscript, "Our findings suggest, however..." sounds as an unnecessary generalization and should be made into a weaker statement. One can change "could not serve" -> "unlikely to serve" for example. Outside of this issue I thank the author for the detailed answer and recommend the manuscript for publication
Report #1 by Anonymous (Referee 2) on 2018-6-1 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1705.03956v4, delivered 2018-06-01, doi: 10.21468/SciPost.Report.482
Report
In this revised version, the author properly answers most of my previous questions. The draft contains a thorough study on different generalizations of SYK models and is of high quality. Now I suggest the publication of this draft.
Nevertheless, I still have difficulty understanding the equation 45 and 48 in this revised draft although the author have explained a lot in the reply. For example, in the Lorentz invariant case (48), why the reparametrization field appears as (\partial_\mu \epsilon^\mu)^2 instead of \epsilon_\mu \partial^2 \epsilon^\mu? Why we have a factor k_\mu^{D/2} here? Similar questions can be asked for Eq. 45. I think it may be helpful to explain this in more details or add some references.
Anonymous on 2018-06-21 [id 277]
(in reply to Report 1 on 2018-06-01)
Answering the comments by Referee 1:
"Nevertheless, I still have difficulty understanding the equation 45 and 48 in this revised draft although the author have explained a lot in the reply. For example, in the Lorentz invariant case (48), why the reparametrization field appears as (\partial_\mu \epsilon^\mu)^2 instead of \epsilon_\mu \partial^2 \epsilon^\mu? Why we have a factor k_\mu^{D/2} here? Similar questions can be asked for Eq. 45. I think it may be helpful to explain this in more details or add some references."
Author's reply:
It is indeed true that the corresponding quadratic forms might be more general than the ones presented in the schematic effective actions (45,48). In the revised version, we replaced those with the most general expressions that are quadratic in frequency and momentum (Lorentz invariance does impose some restrictions, though) and provided the necessary comments, following the above equations.
Anonymous on 2018-06-21 [id 276]
(in reply to Report 2 on 2018-06-13)Answering the comments by Referee 2:
"In the revised version the author answers my questions and implements changes except the last one suggested. I should have been more precise in the request. To me the pre-last paragraph of the manuscript, "Our findings suggest, however..." sounds as an unnecessary generalization and should be made into a weaker statement. One can change "could not serve" -> "unlikely to serve" for example. Outside of this issue I thank the author for the detailed answer and recommend the manuscript for publication."
As per the referee's advice, we somewhat softened the language of our final conclusions.