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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 | |
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| Preprint Link: | https://arxiv.org/abs/2310.14877v2 (pdf) |
| Date accepted: | July 9, 2024 |
| Date submitted: | June 22, 2024, 2:21 a.m. |
| Submitted by: | Dongmin Gang |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| 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.
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Author comments upon resubmission
List of changes
Here are the changes of manuscript and replies to the referees’ suggestions.
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We added a comment below equation (3.15) noting that the first two characters can be expressed as Nahm sums after rescaling m1.
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We mentioned below equation (3.28) that c_{eff} is always 1.
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We provided the sizes of the modular matrices in equations (2.19), (2.29), and (2.30).
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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.
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We added more explanations about the Haagerup-Izumi modular data below equation (2.32).
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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).
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We corrected a typo in the K matrix in equation (3.24); the first entry should be 8 instead of 4.
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In section 3.3, we included the explicit q-series of the characters up to some orders.
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In equations (2.1) and (2.4), we specified whether we are using N=3 or N=2 CS terms in the gauging.
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At the beginning of section (2.1.3), we added a paragraph stating that the S-fold SCFTs are associated with once-punctured torus bundles in 3D-3D correspondence.
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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 non-unitary TQFTs or their boundary RCFTs. This would be an interesting direction for future research.
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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.
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We replaced "a.k.a" with "also known as" and spelled out "vvmf" as "vector-valued modular form" when it first appeared.
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We numerically checked the S-transformation 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).
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Below equation (3.38), we added a brief introduction to the Bantay-Gannon method.
Published as SciPost Phys. 17, 064 (2024)
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