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Constructing the Infrared Conformal Generators on the Fuzzy Sphere
by Giulia Fardelli , Andrew Liam Fitzpatrick , Emanuel Katz
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Submission summary
| Authors (as registered SciPost users): | Giulia Fardelli |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202411_00016v2 (pdf) |
| Date accepted: | 2025-02-27 |
| Date submitted: | 2025-01-22 16:48 |
| Submitted by: | Fardelli, Giulia |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We investigate the conformal algebra on the fuzzy sphere, and in particular the generators of translations and special conformal transformations which are emergent symmetries in the infinite IR but are broken along the RG flow. We show how to extract these generators using the energy momentum tensor, which is complicated by the fact that one does not have a priori access to the energy momentum tensor of the CFT limit but rather must construct it numerically. We discuss and quantitatively analyze the main sources of corrections to the conformal generators due to the breaking of scale-invariance at finite energy, and develop efficient methods for removing these corrections. The resulting generators have matrix elements that match CFT predictions with accuracy varying from sub-percent level for the lowest-lying states up to several percent accuracy for states with dimension $\sim 5$ with $N=16$ fermions. We show that the generators can be used to accurately identify primary operators vs descendant operators in energy ranges where the spectrum is too dense to do the identification solely based on the approximate integer spacing within conformal multiplets.
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 have fixed typos and extraneous equation numbers.
We have reviewed the notation in appendix D to make it consistent.
We have added clarification comments to address the referees' requests:
- We have added a comment in the summary about when high-dimension limits are expected to start to emerge
- We added a definition of $\tilde{\Lambda}$ on page 16, immediately after it first appears
-We have added an appendix summarizing the dimensions emerging from our analysis as suggested by the referees
Published as SciPost Phys. 18, 086 (2025)
Reports on this Submission
Report
The authors addressed my question and mentioned explicitly an example of a model in which their study could be applied to match results obtained via EFT methods.
I believe this adds to their motivation for future research, and I recommend the paper for publication.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report
The authors have addressed a number of my comments, for which I thank them.
On page 25, in the paragraph under equation (5.2), they have rephrased the cutoff (which allowed for negative scaling dimensions, as can be seen in figure 10) as "optimistic". I want to state, for the record, that any cutoff that allows for negative scaling dimensions is more than just "optimistic".
That being said, given that the authors have addressed most of my complaints, I recommend the paper for publication.
Recommendation
Publish (meets expectations and criteria for this Journal)
Report #1 by Connor Behan (Referee 1) on 2025-2-16 (Invited Report)
Report
The authors have recently made corrections and added statements which give more context to the results. I appreciate these and think that the paper is ready now.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)