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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 | |
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| Preprint Link: | https://arxiv.org/abs/2307.13454v3 (pdf) |
| Date submitted: | 2024-02-26 00:08 |
| Submitted by: | Ghodrati, Mahdis |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We present the connections between the behaviors of string scattering amplitudes and mutual information, in several holographic confining backgrounds. 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. Next, we discuss 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.
Current status:
Reports on this Submission
Report
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. 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.
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. 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. In my opinion, the manuscript is not successful in doing so.
Therefore, in my opinion, the main finding in the manuscript is shaky. 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.
Report 1 by Maurizio Firrotta on 2024-4-6 (Invited Report)
Report
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.
*)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.
*)page 18, line 6 below formula (5.6) there is a missprint:
ransom matrix -> random matrix
*)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.
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.