SciPost Submission Page
Anomalous Continuous Translations
by Nathan Seiberg
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Submission summary
| Authors (as registered SciPost users): | Nathan Seiberg |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2412.14434v2 (pdf) |
| Date submitted: | April 9, 2025, 6:26 p.m. |
| Submitted by: | Nathan Seiberg |
| Submitted to: | SciPost Physics |
| for consideration in Collection: |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We discuss a large class of non-relativistic continuum field theories where the Euclidean spatial symmetry of the classical theory is violated in the quantum theory by an Adler-Bell-Jackiw-like anomaly. In particular, the continuous translation symmetry of the classical theory is broken in the quantum theory to a discrete symmetry. Furthermore, that discrete symmetry is extended by an internal symmetry, making it non-Abelian. This presentation streamlines and extends the discussion in [1]. In an Appendix, we present an elementary introduction to 't Hooft and Adler-Bell-Jackiw anomalies using a well-known system.
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
Current status:
Has been resubmitted
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2025-7-14 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2412.14434v2, delivered 2025-07-14, doi: 10.21468/SciPost.Report.11567
Strengths
Original, pedagogical, timely
Weaknesses
None.
Report
This paper presents a short but very pedagogical and insightful discussion of anomalies of continuous translation symmetries - how these can be in some cases broken to a discrete symmetry in the quantum theory. The author avoids use of fancy mathematical language, and provides enjoyable examples in appendices. Moreover relationships with other aspects - in particular the LSM theorem - are discussed and inspiring ideas put forward. Overall, this is a very nice, very smart paper. I noticed a few misprints, already mentioned by the first referee.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
Report #1 by Anonymous (Referee 1) on 2025-7-13 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2412.14434v2, delivered 2025-07-13, doi: 10.21468/SciPost.Report.11563
Strengths
The paper presents a very streamlined discussion on the breaking of continuous translation symmetries in QFT to discrete (non-abelian) translation symmetries due to the presence of nontrivial background gauge field and an ABJ-like anomaly. Along the way, the author addresses puzzles concerning such discrete translation symmetries and their anomalies which were studied previously.
The author's approach gives a unified perspective on this phenomena using a Chern-Simons type action for several different classes of models (e.g. abelian gauge theories and non-linear sigma models) and also connects to modern perspectives on symmetries and anomalies.
The presentation is very pedagogical: the author is able to convey the message without getting into the details of differential cohomology (which is the proper math framework for questions here but can be overwhelming for many physicists).
The author's approach gives a unified perspective on this phenomena using a Chern-Simons type action for several different classes of models (e.g. abelian gauge theories and non-linear sigma models) and also connects to modern perspectives on symmetries and anomalies.
The presentation is very pedagogical: the author is able to convey the message without getting into the details of differential cohomology (which is the proper math framework for questions here but can be overwhelming for many physicists).
Weaknesses
None
Report
The journal's acceptance criteria are met and I recommend publication in SciPost after addressing the small changes below.
Requested changes
Here I list some small changes to be made (mostly typos):
- (3.10) is repetitive with (3.7). The author may just want to refer to the d=1 case of (3.7) here and comment on the general case in words (already given in (3.7)).
- end of second paragraph on pg 15: "of-shell"
- first paragraph in conclusion: "one turns one"
- obvious typo in (A.4) second equation
- (A.8): "=->"
- p25 second bullet point: "Gcalssical"
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
Author: Nathan Seiberg on 2025-07-13 [id 5640]
(in reply to Report 1 on 2025-07-13)I thank the referee for the positive comments and for catching all these typos. All of them will be fixed.