SciPost Submission Page
Studying the 3d Ising surface CFTs on the fuzzy sphere
by Zheng Zhou, Yijian Zou
Submission summary
| Authors (as registered SciPost users): | Zheng Zhou |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202411_00019v1 (pdf) |
| Date accepted: | 2024-12-05 |
| Date submitted: | 2024-11-07 20:43 |
| Submitted by: | Zhou, Zheng |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Boundaries not only are fundamental elements in nearly all realistic physical systems, but also greatly enrich the structure of quantum field theories. In this paper, we demonstrate that conformal field theory (CFT) with a boundary, known as surface CFT in three dimensions, can be studied with the setup of fuzzy sphere. We consider the example of surface criticality of the 3D Ising CFT. We propose two schemes by cutting a boundary in the orbital space or the real space to realise the ordinary and the normal surface CFTs on the fuzzy sphere. We obtain the operator spectra through state-operator correspondence. We observe integer spacing of the conformal multiplets, and thus provide direct evidence of conformal symmetry. We identify the ordinary surface primary $o$, the displacement operator $\mathrm{D}$ and their conformal descendants and extract their scaling dimensions. We also study the one-point and two-point correlation functions and extract the bulk-to-surface OPE coefficients, some of which are reported for the first time. In addition, using the overlap of the bulk CFT state and the polarised state, we calculate the boundary central charges of the 3D Ising surface CFTs non-perturbatively. Other conformal data obtained in this way also agrees with prior methods.
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 both referees for their careful reading of our manuscript, their appreciation of our work as well as their useful comments and concerns. In the revised version, we improved the clarity of the manuscript based on the Referees' suggestions.
We have given a point-by-point response to the comments of both Referees. We believe that the changes made have further improved our paper and we hope that the current manuscript will be considered suitable for further consideration in SciPost Physics.
List of changes
* We have added a paragraph to the Introduction section to introduce 3d CFTs in general and define related concepts.
* We have revised the second paragraph on Page 4 to define the mentioned operators and specify some detail.
* We have revised Table 1 to include previous results.
* We have revised the first and second paragraphs on page 6 to emphasise the significance of this paper and clarify the scheme we use for calculation.
* We have revised Page 8 to be more precise about the schemes we use.
* We have added Footnote 4 to Page 10 to explain why the speed of light is the same in the bulk and surface CFT.
* We have revised the caption of Figures 6, 8 and 11, and added Footnote 5 to specify the prediction to the correlation functions by conformal symmetry that we compare with.
* We have revised the notations on Page 15 to be more consistent.
* We have added Footnote 8 to explain the subleading contributions in Table 2.
* We have added a paragraph to Page 19 to explain the relation between the overlap and the partition function.
* We have added Footnote 9 to explain the subleading contributions in Figure 14.
* We have revised the second paragraph in the Discussion section to discuss the realisation of special surface CFT.
* We have revised the Appendices to clarify their purposes and link to the main text.
* We have added Appendix C.2 to compare scaling dimensions under different calibrations.
* We have done a thorough proofreading to improve the clarity and fix the grammatical errors.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Reports on this Submission
Report
The authors have addressed the points from my first report, and the responses on all points are satisfactory. In the case of the first comment, regarding the speed of light in the bulk vs in the boundary, I think they are technically correct in that in the IR limit, Lorentz invariance reemerges and the speed of light is the same in the bulk in the boundary. However, at any finite volume, this symmetry is only approximate, so that the speed of light in the bulk and boundary will not be the same. I think they could improve the rate of convergence of their results by taking this into account and rescaling the dimension of the displacement operator to be 3. Since in principle this should only affect the rate of convergence and not the final extrapolated value, I think it is not strictly necessary and I leave it to the authors' discretion, and recommend the paper for publication either way.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)