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Brane Detectors of a Dynamical Phase Transition in a Driven CFT
by Suchetan Das, Bobby Ezhuthachan, Arnab Kundu, Somnath Porey, Baishali Roy, Krishnendu Sengupta
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Submission summary
| Authors (as registered SciPost users): | Arnab Kundu · Krishnendu Sengupta |
| Submission information | |
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| Preprint Link: | scipost_202212_00071v1 (pdf) |
| Date submitted: | 2022-12-26 07:00 |
| Submitted by: | Kundu, Arnab |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We show that a dynamical transition from a non-heating to a heating phase of a periodic SL(2,ℝ) driven two-dimensional conformal field theory (CFT) with a large central charge is perceived as a first order transition by a bulk brane embedded in the dual AdS. We construct the dual bulk metric corresponding to a driven CFT for both the heating and the non-heating phases. These metrics are different AdS2 slices of the pure AdS3 metric. We embed a brane in the obtained dual AdS space and provide an explicit computation of its free energy both in the probe limit and for an end-of-world (EOW) brane taking into account its backreaction. Our analysis indicates a finite discontinuity in the first derivative of the brane free energy as one moves from the non-heating to the heating phase (by tuning the drive amplitude and/or frequency of the driven CFT) thus demonstrating the presence of the bulk first order transition. Interestingly, no such transition is perceived by the bulk in the absence of the brane. We also provide explicit computations of two-point, four-point out-of-time correlators (OTOC) using the bulk picture. Our analysis shows that the structure of these correlators in different phases match their counterparts computed in the driven CFT. We analyze the effect of multiple EOW branes in the bulk and discuss possible extensions of our work for richer geometries and branes.
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Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2023-5-23 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202212_00071v1, delivered 2023-05-23, doi: 10.21468/SciPost.Report.7236
Report
Authors consider quantum dynamics in 2d CFTs generated by action of a unitary build from the global SL(2,R) sub-algebra (two copies) on the vacuum state. Physically, this can be interpreted as an inhomogeneous quantum quench or a periodic Floquet drive. This has been studied in various examples and, depending on the parameters of the evolving Hamiltonian, a dynamical transition between a heating and non-heating phases was observed.
The main contribution of this work is a holographic proposal or interpretation of such proces in holographic 2d CFTs (since these states and operators are completely universal, there is no distinction between holographic and non-holographic 2d CFTs). Authors identify the SL(2,R) generators in the effective Floquet Hamiltonian with the SL(2,R) generators in AdS3 and find a local frame in which this operator generates time translations “s”. This is interesting (new or standard?) and may give some hints on local frames in the bulk (e.g. see 2211.16512 [hep-th]).
The crucial part of the holographic picture is played by the “EOW” branes that are chosen as constant mean curvature slices of AdS3. Authors compute gravity action (in the probe limit as well as with back-reaction) and argue that it can distinguish between the different phases.
I find the paper interesting and worth publishing after addressing a few minor comments:
1. Acting with the unitary on some more non-trivial highest weight state would be much more interesting and would involve more input about holographic CFT (large c, sparseness). Was it too difficult to analyse?
2. The action with the probe brane as well as the CMC slices played a key role in arXiv:2104.00010v2 [hep-th]. In fact the general construction is quite similar and, modulo some boundary-terms one could interpret the bulk computation that distinguishes the phases as holographic path-integral complexity… Maybe worth exploring or commenting on the connection.
3. On a related note, after back-reaction one may think about the bulk setup as an example of the AdS/BCFT framework. Is there any sign of this from the CFT perspective (given that its just a quench in ordinary CFT without any boundaries)?
4. Above (2.12) it should be “c_1 = tan φ” and not $\phi_1$. Btw, where does this come from? How do they know that this constant should become one of the “bulk coordinates”.
5. Maybe some Hamiltoni-Jacobi perspective could be useful for the previous question?
6. What does the dot “.” in (A.1) mean?
Report #1 by Anonymous (Referee 2) on 2023-3-12 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202212_00071v1, delivered 2023-03-12, doi: 10.21468/SciPost.Report.6884
Report
This paper studies non-heating to heating transitions in 2d CFTs using holographic descriptions involving gravity+brane systems. A general effective Hamiltonian mapped to its AdS3 representation (sec.2) leads to bulk curves generated correspondingly, parametrized by some stroboscopic time s, and corresponding coordinate solutions (in the non-heating, heating and transition phases). Appropriate codim-1 probe brane embeddings via these coordinate solutions (sec.3) then shows a difference in the brane on-shell action regarded as free energy. Further studies are carried out via end-of-world branes as diagnostics: these reveal various detailed differences (stemming from EOW-brane extrinsic curvature effects here). The authors then study boundary 2-point correlation functions (sec.4) via bulk geodesic approximations and 2d CFT on the appropriate boundary slice, which match in appropriate regimes. Subsequently they study OTOCs.
I find the paper interesting, comprehensive in what it studies, and worth publication.
I have a few questions, some of which appear listed in the Discussion section:
(1) The class of Hamiltonians considered is not the most general: it would be interesting to understand these generalizations. It would seem some of these will have nontrivial time-dependence, which may be interesting for various purposes.
(2) The AdS2 slicing plays crucial roles: this appears special. Naively, general foliations might suggest the 2d slices being conformally AdS2 (which would be rather different). These choices of AdS2 slices might dovetail with particular "static gauge" choices for the probe branes (in eqs.3.11-3.12 via $\ \sigma_0=s,\ \sigma_1=\theta$), but it's not clear to me if this is true in general, going from the considered boundary metrics to the bulk. I'm wondering if this links back to (1) above.
(3) Besides correlation functions, an obivous probe of such phenomena is entanglement entropy. In the holographic context, the corresponding RT/HRT surfaces will amount to geodesics, but with various differences in the thinking. It may be interesting to explore this as well as the generalized entropy (via appropriate quantum extremal surfaces). There may also be useful things to gain from studying double holography.
Additionally, for completeness, perhaps it will be useful to add the following in whatever way the authors deem fit:
(a) a little more elaboration on the AdS3 representations of the CFT Hamiltonian, the three phases and the sign of d.
(b) some detail on the coordinate solutions to eqs.2.7-2.9, possibly in an Appendix (perhaps also including a short review of this, e.g. from ref.[60]?).