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A nonunitary bulkboundary correspondence: Nonunitary Haagerup RCFTs from Sfold SCFTs
by Dongmin Gang, Dongyeob Kim, Sungjay Lee
Submission summary
Authors (as registered SciPost users):  Dongmin Gang 
Submission information  

Preprint Link:  https://arxiv.org/abs/2310.14877v2 (pdf) 
Date accepted:  20240709 
Date submitted:  20240622 02:21 
Submitted by:  Gang, Dongmin 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We introduce a novel class of twodimensional nonunitary rational conformal field theories (RCFTs) whose modular data are identical to the generalized HaagerupIzumi modular data. Via the bulkboundary correspondence, they are related to the threedimensional nonunitary Haagerup topological field theories, recently constructed by a topological twisting of threedimensional ${\cal N}=4$ rankzero superconformal field theories (SCFTs), called Sfold SCFTs. We propose that, up to the overall factors, the halfindices of the rankzero SCFTs give the explicit Nahm representation of four conformal characters of the RCFTs including the vacuum character. Using the theory of BantayGannon, we can successfully complete them into the full admissible conformal characters of the RCFTs.
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 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 multipronged followup work
 Detail a groundbreaking theoretical/experimental/computational discovery
 Present a breakthrough on a previouslyidentified and longstanding research stumbling block
Author comments upon resubmission
List of changes
Here are the changes of manuscript and replies to the referees’ suggestions.
1. We added a comment below equation (3.15) noting that the first two characters can be expressed as Nahm sums after rescaling m1.
2. We mentioned below equation (3.28) that c_{eff} is always 1.
3. We provided the sizes of the modular matrices in equations (2.19), (2.29), and (2.30).
4. The modular matrices in (2.19) were obtained in the reference [7], where the SL(2,Z) relations were checked for various values of k using Mathematica.
5. We added more explanations about the HaagerupIzumi modular data below equation (2.32).
6. We added a comment below equation (3.54) noting that the characters of R_{k=4} are related to the characters of the supersymmetric N=1 minimal model SM(2,12).
7. We corrected a typo in the K matrix in equation (3.24); the first entry should be 8 instead of 4.
8. In section 3.3, we included the explicit qseries of the characters up to some orders.
9. In equations (2.1) and (2.4), we specified whether we are using N=3 or N=2 CS terms in the gauging.
10. At the beginning of section (2.1.3), we added a paragraph stating that the Sfold SCFTs are associated with oncepunctured torus bundles in 3D3D correspondence.
11. The SL(2,Z) relations of modular matrices are only satisfied in the topological twisting limits, i.e. (m,\nu) = (0, \pm 1). Currently, we do not know how to interpret the deformations from the perspective of nonunitary TQFTs or their boundary RCFTs. This would be an interesting direction for future research.
12. From the bulk computation, we can determine the exponents (Delta_alpha) only modulo 1, and we present the values modulo 1 in equation (3.13). Developing a systematic methodology to fully determine the exponents would be an interesting future work.
13. We replaced "a.k.a" with "also known as" and spelled out "vvmf" as "vectorvalued modular form" when it first appeared.
13. We numerically checked the Stransformation property of the characters by evaluating them at ττ near ii, where both q=e^{2\pi i \tau} and tilde{q} =exp(2pi i (1/\tau)) are smaller than 1. We added a related comment below equation (3.27).
14. Below equation (3.38), we added a brief introduction to the BantayGannon method.
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 successfully addressed the concerns and suggestion. These revisions have significantly improved the clarity of the manuscript. I am pleased to recommend the revised manuscript for publication.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)