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Chaotic Correlation Functions with Complex Fermions
by Ritabrata Bhattacharya, Dileep P. Jatkar, Arnab Kundu
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Submission summary
| Authors (as registered SciPost users): | Ritabrata Bhattacharya · Dileep Jatkar · Arnab Kundu |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1810.13217v4 (pdf) |
| Date accepted: | 2021-05-31 |
| Date submitted: | 2021-02-24 05:29 |
| Submitted by: | Bhattacharya, Ritabrata |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study correlation functions in the complex fermion SYK model. We focus, specifically, on the h = 2 mode which explicitly breaks conformal invariance and exhibits the chaotic behaviour. We explicitly compute fermion six-point function and extract the corresponding six-point OTOC which exhibits an exponential growth with maximal chaos. Following the program of Gross-Rosenhaus, this correlator contains information of the bulk cubic coupling, at the conformal point as well as perturbatively away from it. Unlike the conformal modes with high values of h, the h = 2 mode has contact interaction dominating over the planar in the large q limit.
List of changes
1. The notation for Euclidean time in Section 5 is now changed to \tau so that there is no confusion with the Lorentzian time ` t '.
2. The arguments \theta_1,...,\theta_6 for the 2-fold case are now chosen more carefully so as to ensure that the operator ordering does not change when \theta_1 is changed.
3. A comment in the Conclusion section is added to remark that the result we obtain is the Lyapunov growth at ``early time".
Published as SciPost Phys. Core 4, 018 (2021)
Reports on this Submission
Weaknesses
1- Poor presentation
Report
Based on the previous and current version of this manuscript and the presentation and the results discussed in this paper I would recommend it for publication in SciPost Core journal. I believe that some of the results in this paper might be useful for the community working on related topics.
Report
My previous points have been addressed. I am still somewhat skeptical about how much OTOC physics the numerical method captures (even at early times), but the phrasing of the manuscript is now sufficiently conjectural to reflect this. I would recommend publication of the article in its current form in the SciPost Physics Core journal.