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On the relation between fractional charge and statistics
by T. H. Hansson, Rodrigo Arouca, Thomas Klein Kvorning
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Submission summary
| Authors (as registered SciPost users): | Rodrigo Arouca · Thors Hans Hansson |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2412.15857v2 (pdf) |
| Date submitted: | March 3, 2025, noon |
| Submitted by: | Rodrigo Arouca |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We revisit an argument, originally given by Kivelson and Ro\v{c}ek, for why the existence of fractional charge necessarily implies fractional statistics. In doing so, we resolve a contradiction in the original argument, and in the case of a $\nu = 1/m$ Laughlin holes, we also show that the standard relation between fractional charge and statistics is necessary by an argument based on a t'Hooft anomaly in a one-form global ${\mathcal Z}_m$ symmetry.
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
We removed the repeated sentences indicated by one of the referees.
Current status:
Has been resubmitted
Reports on this Submission
Report #1 by Anonymous (Referee 2) on 2025-4-25 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2412.15857v2, delivered 2025-04-25, doi: 10.21468/SciPost.Report.11078
Strengths
1- The important problem of the relationship between fractional charge and statistics is revisited with new insights arising from the ’t Hooft anomaly of a 1-form symmetry.
2- Previous heuristic arguments are discussed, and the loopholes in those arguments are carefully examined.
3- A rigorous argument is presented to explain the impossibility of having strictly local excitations with fractional charge.
2- Previous heuristic arguments are discussed, and the loopholes in those arguments are carefully examined.
3- A rigorous argument is presented to explain the impossibility of having strictly local excitations with fractional charge.
Weaknesses
1- I find the article somewhat convoluted and not sufficiently clear in its presentation.
Report
To elaborate on point 1: it would be helpful for the formal part of the manuscript to be self-contained. The argument begins with Eq. (1), after which the relevant assumptions should be clearly stated, and the “flux removal” procedure explained at the formal level. It should then be demonstrated that this removal renders the theory inconsistent due to the anomaly. While all of these elements are present in the derivation, their presentation is far from straightforward.
To conclude, I believe the manuscript is suitable for publication in SciPost Physics in its current form. However, I (and, hopefully, the readers) would appreciate a clearer exposition of the formal argument connecting fractional charge to fractional statistics.
To conclude, I believe the manuscript is suitable for publication in SciPost Physics in its current form. However, I (and, hopefully, the readers) would appreciate a clearer exposition of the formal argument connecting fractional charge to fractional statistics.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Author: Rodrigo Arouca on 2025-05-12 [id 5470]
(in reply to Report 1 on 2025-04-25)We thank the referee for thoroughly reading our manuscript, and making a relevant point about the presentation. We are pleased that they find it suitable for publication in SciPost. We agree that we should have explained the intent and logic of the formal derivation better, and also made a clearer separation from the initial intuitive discussion. We have reformulated the text above eq. 1 to smooth the transition between the two parts of the paper.