SciPost Submission Page
The random free field scalar theory
by Alessandro Piazza, Marco Serone, Emilio Trevisani
Submission summary
| Authors (as registered SciPost users): | Alessandro Piazza · Marco Serone · Emilio Trevisani |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202409_00029v2 (pdf) |
| Date submitted: | 2024-12-06 10:28 |
| Submitted by: | Serone, Marco |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Quantum field theories with quenched disorder are so hard to study that even exactly solvable free theories present puzzling aspects. We consider a free scalar field $\phi$ in $d$ dimensions coupled to a random source $h$ with quenched disorder. Despite the presence of a mass scale governing the disorder distribution, we derive a new description of the theory that allows us to show that the theory is gapless and invariant under conformal symmetry, which acts in a non-trivial way on $\phi$ and $h$. This manifest CFT description reveals the presence of exotic continuous symmetries, such as nilpotent bosonic ones, in the quenched theory. We also reconsider Cardy's CFT description defined through the replica trick. In this description, the nilpotent symmetries reveal a striking resemblance with Parisi-Sourlas supersymmetries. We provide explicit maps of correlation functions between such CFTs and the original quenched theory. The maps are non-trivial and show that conformal behaviour is manifest only when considering suitable linear combinations of averages of products of correlators. We also briefly discuss how familiar notions like normal ordering of composite operators and OPE can be generalized in the presence of the more complicated local observables in the quenched theory.
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
Author comments upon resubmission
We thank the editor for the quick response. Below we reply to the editor's comments.
- ``Your paper can be relevant as a pedagogical introduction of how $O(-2)$ appears; but this observation is not new. (You can simply put the coupling to zero in the cited and other work.)"
We do not think that our paper can be relevant just as an introduction to $O(-2)$ symmetry. This is never said neither in the paper, nor in any of our replies to the referees. It's in fact the other way around. We stress several times in our paper that $O(-2)$ was known. For example, we write in the introduction, first paragraph at page 5, ``While some symmetries, like $O(-2)$ and additional $\bf{Z}_2$ symmetries, are quite obvious and were already considered in [13, 14, 18], we show that new less trivial symmetries are present."
The novelty of our paper is well described in the abstract of the paper, which we invite the editor to carefully read.
- ``In order that it is as pedagogical as possible, make the changes below."
The clarity and pedagogical value of our paper was clearly indicated by both referees.
- ``Make clear how your work relates to the literature."
In addition to the changes implemented to comply with the referee's requests, we added footnote 3 where we refer the reader for comparisons with previous literature. As we explained in the reply to the second referee, our paper is theoretical in nature and no RG flow is present. We believe that an emphasis on comparisons would be misleading and improper.
- " (ii) add a section on supersymmetry in the Parisi-Sourlas variables."
The paper actually already contains a section about Parisi-Sourlas supersymmetry written in the SUSY variables, like in the original paper. For reference, the section is called ``Parisi-Sourlas supersymmetry" and can be found in the index of the paper (sec.4.3.3).
- ``Another paper not yet cited is Nucl. Phys. B 946 (2019) 114696."
We added this paper to our reference list.
We hope that the revised version of the manuscript will be accepted for publication.
Current status:
Reports on this Submission
Strengths
The manuscript introduces and studies a simple, exactly solvable model in a relatively pedagogical manner.
Weaknesses
1. It is not completely clear how this toy model can be practically useful for studying the interacting case, which is a really complex problem.
2. As a consequence, it is difficult to reconcile with other methods, particularly FRG and non-perturbative RG, since they can be applied only to the interacting case.
Report
The authors have clarified almost all the points raised in my first report. When I asked about the possibility of computing the critical order parameter distribution, I was referring to the entire distribution, similar to what was done in S. T. Bramwell et al., Phys. Rev. Lett. 84, 3744 (2000), and I. Balog, A. Rançon, and B. Delamotte, Phys. Rev. Lett. 129, 210602 (2022), rather than just the first moment, which trivially vanishes.
The authors have improved the manuscript, and I can recommend the revised version for publication in SciPost.
Recommendation
Publish (meets expectations and criteria for this Journal)
Strengths
Same as in my first report
Report
The authors have satisfactorily responded to my comments and in my opinion to the other referee comments. I therefore recommend publication of the revised version.
Recommendation
Publish (meets expectations and criteria for this Journal)