SciPost Submission Page
String amplitudes and mutual information in confining backgrounds: the partonic behavior
by Mahdis Ghodrati
Submission summary
| Authors (as registered SciPost users): | Mahdis Ghodrati |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2307.13454v5 (pdf) |
| Date submitted: | 2024-05-01 06:41 |
| Submitted by: | Ghodrati, Mahdis |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
In the background of several holographic confining backgrounds, we present the connections between the behaviors of string scattering amplitudes and mutual information. We lay down the analogies between the logarithmic branch cut behavior of the string scattering amplitude in $4d$, $ \mathcal{A}_4 $, at low and medium Mandelstam variable $s$ observed in \cite{Bianchi:2021sug}, which is due to the dependence of the string tension on the holographic coordinate, and the branch cut behavior observed in mutual information and critical distance $D_c$ at low-cut-off variable $u_{KK}$ studied in our previous work \cite{Ghodrati:2021ozc}. It can also be seen that in both cases, as $s$ or $u_{KK}$ increases, the peaks in the branch cuts fade away in the form of $\text{Re}\lbrack \mathcal{A}_4 \rbrack \propto s^{-1}$. Then, we used modular flow and modular Hamiltonian as intermediary concept to further clarify the observed connection. We discussed how mutual information itself can detect chaos in various scenarios. In addition, we considered two examples of Compton scattering between two photons and also the decay of a highly excited string into two tachyons and scrutinized the pattern of entanglement entropy and the change in the mutual information in these examples. Then, the kink-kink and kink-antikink scatterings as simple models of scattering in confining geometries have been used to examine the fractal structures in the scatterings of topological defects. Finally, the relationships between Regge conformal block and quantum error correction codes through pole-skipping and chaos bound have been postulated. These observed connections can further establish the ER$=$EPR conjecture and the general interdependence between the scattering amplitudes and entanglement entropy.
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
List of changes
I addressed all the critics of my first referee. Explained further why mutual information, string amplitude, and chaos in confining geometries should be related using the mathematical relations for the connections between entanglement entropy and scattering amplitude.
I also explained how modular Hamiltonian should come into play. Also add a few figures to explain my setup better to show how the end-wall of confining geometry causes the appearance of chaos.
Also, I added a few references.
Current status:
Reports on this Submission
Report
I would like to thank the author for responding to my comments. However, in my opinion, the validity of the paper has not been improved significantly. The author has not provided mathematically sound argument for the erratic behavior shown in the mutual information plots, but rather referred to discussion of "modular chaos" in the literature. It seems to me that the discussion of modular chaos mostly concern the property of correlation functions under modular flow, which is not obviously related to the phenomena discussed in the manuscript.
Recommendation
Reject
Anonymous on 2024-05-01 [id 4459]
This is the editor in charge. Here I present the response of the author to the referees in the first round.
To Anonymous Report 2
In this manuscript, the author studied the connection between string amplitudes and mutual information in holographic confining backgrounds. The main finding, as the author summarized in the introduction section, is a certain analogy between (1) the dependence of the critical distance D_c as a function of the IR scale u_{KK} of the confining theory, and (2) the scattering amplitude as a function of the Mandelstam variable s. To help clarify this analogy, the author further drew connections to a several other phenomena, including modular flow, quantum error correction codes, etc. Despite the intriguing claims and the possibility of tying several fields together, I’m not convinced by the analogy the author is trying to propose. For one, the figures 2, 3, 4 and 5 seem very suspicious. To elaborate, the physical quantity being considered is the mutual information between two spatial slabs separated by distance D, in a confining theory with (inverse) mass scale u_{KK}. As is well known, as one increases the distance D, there is a phase transition happening at D_c where the RT surface of the two slabs become disconnected, and therefore the mutual information vanishes in the large N limit. One would naturally expect, since the metric depends on u_{KK} in a simple and analytic way, the quantity D_c would be an (at lease piecewise) analytic function of u_{KK}. However, figure 2 shows the dependence is highly non-analytic and fluctuating. I can only find the same behavior in a previous paper by the same author and no clear mathematic explanation for the erratic behavior is given.
Please note that the monotonic decreasing behavior, by increasing the distance between the slabs, are only for the case without an end-wall in the background geometry (conformal case). When there is a hard end-wall or soft wall as in the case of confining geometries, this create the “modular chaos”, which its effects can be detected through mutual information. One could imagine modular waves being sourced from the two entangled mixed subregions which hit the end-wall and then getting scattered back, creating modular chaos which form the specific peak structures in the plots of mutual information that we have observed here. The concept of modular chaos for different setups have been discussed further in 2004.08383, where the discrete structures have been detected there too. Note that it has been demonstrated, for instance in 1912.02810, that the modular chaos as in the case of entanglement (and mutual information) can reconstruct the holographic bulk geometry. In 2111.12106, the connections between chaos and peak structures of string amplitude have been discussed. So, the peak structures of string amplitude and entanglement structures should be connected with each other through chaos and specially the “modular chaos”, as we have showed in our work here. I have added these new comments to the paper.
On the other hand, the way the lines are broken in figures 2, 3, 4 and 5 appear to be a typical feature of instability in numerical integrations. With no quantitative equations and physical interpretation to back up, these plots appear suspicious and significantly weaken the findings that are based on it.
The physical equation can be derived from relation 3.3, (delta S_E sim (log s/t)^2) which connects the entanglement entropy with scattering amplitude. It has a logarithmic function and a zero based on the relation. Then, the change of “mutual information” can be written in this way in terms of the Mandelstam’s variables, and from that one can see the mutual information should also have “zeros” or “peaks” in its behavior, similar to the case of scattering amplitude as we have seen in our plots. The physical interpretation, as explained in the previous part, is related to the “modular chaos” and the presence of an end-wall in the geometry which by reflecting the modular waves create this chaos along the holographic radial coordinate and the chaotic behavior decay across the geometry, which are being caught by the behavior of the peaks. Nonetheless, let’s suppose the dependence of D_c on u_{KK} is indeed erratic and has the features as the plots are showing, the connection to the scattering amplitude still appears to be vague. The connections proposed include the branch cut structures as well as the asymptotic fall-off of the two functions. Neither of these were demonstrated with clear quantitative analysis in the manuscript, but rather established by inspecting the plots. Please note that all of the section 4 is for establishing this relation. Again, the connections between entanglement entropy and scattering amplitude have actually been established before, especially in 1404.0794. So, extending it to mutual information should be easily perceivable. So, if people could detect chaos in the structure of scattering amplitude in confining backgrounds, based on the behaviors of its zeros, then the mutual information (or accordingly Dc) should also be able to detect such branch cuts behaviors as we have shown here in our plots, and therefore they can detect chaos. We should also note that the quantities that are being compared, D_c versus amplitude A, u_{KK} versus Mandelstam s, have different dimensions, so a direct comparison does not appear meaningful without clear physical justification. These quantities can become dimensionless easily by using the AdS scale or the energy scales, which we just decided not to do here. Also, note that numerically it is easier to construct the plot of Dc versus uKK rather than the mutual information (I) versus uKK, but they are completely related as Dc is where mutual information becomes zero based on the size of subregions, the distance among them and the distance to the end wall. So, basically, Dc is mutual information itself and both can catch the same details in the holographic geometries. The dimensions can be fixed using the scales in the geometry.
In my opinion, the manuscript is not successful in doing so.
I anticipate by all the explanations here, the ambiguities have been clarified further and things became clearer.
Therefore, in my opinion, the main finding in the manuscript is shaky.
I assume by turning back to the established connections between entanglement entropy and scattering amplitude discussed in previous works, it could become clear that extensions to mutual information and scattering amplitude should be straightforward. I could also point out to the other referee report that mentioned: “The manuscript is valid, well written and well motivated” as extension to mutual information should be discussed too. Apart from this, the overall writing of the manuscript seems to have the tendency of overextending analogies rather than trying to present solid derivations. Based on these, I do not believe it matches the criterion in order to be published on SciPost. I hoped based on my finding, I could discuss the connections of more physical quantities like modular flow, quantum error correction codes, etc as you have mentioned in your comments in the beginning, therefore maybe this paper became rather longer, but I guess it would be beneficial to see the bigger picture where all these quantities get connected. ------------------------------------------------------------------------------------------------------------------------------
To Maurizio Firrotta The manuscript is valid, well written and well motivated. Before recommending for publication, I would suggest some modifications *)Page 1, line 6 from below: the first computation of covariant scattering amplitudes in the DDF formalism was not in reference [16] but in the following reference : Nucl.Phys.B 952 (2020) 114943 I suggest to include the reference and also to be more precise about the literature.
This reference has been added to the paper.
*)Page 16, Chaos in string amplitudes was also recently studied in more general processes: JHEP 04 (2023) 052 2312.02127 2401.02211 I suggest to include the references.
These references have been added.
*)page 18, line 6 below formula (5.6) there is a missprint: ransom matrix -> random matrix Thanks. This is corrected.
*)page 21, line 8 from above: in reference [52] the authors did not find any fractal structure in the string amplitudes, but they had some argument about it. I would like to stress that chaos does not imply automatically fractal structure.
This is corrected.
In reference [54] there is no any definition of chaos in the string decay. The first BRST invariant computation that includes the notion of chaos in the string decay was realized in JHEP 04 (2023) 052. I suggest to include the reference and also to be more precise about the literature.
The reference has been added.