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A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold 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/2310.14877v1 (pdf) |
| Date submitted: | 2024-02-06 06:21 |
| Submitted by: | Gang, Dongmin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We introduce a novel class of two-dimensional non-unitary rational conformal field theories (RCFTs) whose modular data are identical to the generalized Haagerup-Izumi modular data. Via the bulk-boundary correspondence, they are related to the three-dimensional non-unitary Haagerup topological field theories, recently constructed by a topological twisting of three-dimensional ${\cal N}=4$ rank-zero superconformal field theories (SCFTs), called S-fold SCFTs. We propose that, up to the overall factors, the half-indices of the rank-zero SCFTs give the explicit Nahm representation of four conformal characters of the RCFTs including the vacuum character. Using the theory of Bantay-Gannon, we can successfully complete them into the full admissible conformal characters of the RCFTs.
Current status:
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This paper is a very interesting one, where the authors extend their previous results on obtaining 3d non-unitary TQFT from twisting 3d supersymmetric theories by providing their characters by a combination of gauge theory methods and RCFT methods. It easily meets the criteria to be published on SciPost, but a few minor revisions would be welcomed, on the points listed below.
As the referee 1 already wrote a comprehensive report on the side of the non-unitary RCFT, this referee wants to concentrate mostly on the gauge theory part.
- In (2.1), it would be nice to mention that the authors use $\mathcal{N}=3$ Chern-Simons term rather than $\mathcal{N}=2$ Chern-Simons term.
- It would be nice to mention, when going from Sec.2.1.1 to 2.1.2, that the construction (2.1) geometrically corresponds to a once-punctured torus bundle. This fact would be obvious to the practitioners like the authors and this referee but would not be at all obvious.
- Above (2.4), you might want to say that these are $\mathcal{N}=2$ Chern-Simons terms.
- In Sec.2.2 or in the introduction, you might want to mention that the Haagerup-Izumi TQFTs are rather exotic in the sense they are rare examples of TQFTs not related to doubles of finite groups and/or affine Lie algebras.
- The claim (2.16), when considered in reverse, means that the parameters $(m,\nu)$ give deformations of the TQFT data. Is there anything the authors could say about these deformations, other than they exist? For example, do $S$ and $T$ as deformed by $(m,\nu)$ still satisfy the $SL(2,\mathbb{Z})$ relations?
- Around (2.32), it would be nice to explain the notation, the history and the motivations behind these Haagerup-Izumi modular data and the Hecke/Galois transformations. It doesn't have to be long, but the matter-of-factly presentation here could be improved.
- In (3.11), do the authors really mean (3.13)? Don't we need rational numbers without mod 1 here?
- It would be nicer to spell out a.k.a. as "also known as", or vvmf as vector valued modular forms, etc.
- Around (3.28) and elsewhere, the authors say that they study the S-transformation numerically. How do they concretely do that? Do they evaluate the series around $\tau\sim 1$ ? Does the series for $\chi(-1/\tau)$ and $\chi(\tau)$ both converge at that point?
- In Sec.3.3, they explain the Bantay-Gannon method in the sense of how it should be performed, but they do not provide any explanation why it should work. Again the referee understands that the interested readers should refer to the original paper, but a short explanation here would not be bad.
- In the table of $\Xi$ and $\chi$ the authors provide, we see a big block of zeros, say in $\mathcal{R}_{k=8,9,10}$. Is there a simple explanation why?
Report
see the attached pdf