Non-unitary TQFTs from 3D N $$ \mathcal{N} $$ = 4 rank 0 SCFTs
Abstract We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[ T $$ \mathcal{T} $$ rank 0], to a (2+1)D interacting N $$ \mathcal{N} $$ = 4 superconformal field theory (SCFT) T $$ \mathcal{T} $$ rank 0 of rank 0, i.e. having no Coulomb and...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2021)158 |
| _version_ | 1818728905773678592 |
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| author | Dongmin Gang Sungjoon Kim Kimyeong Lee Myungbo Shim Masahito Yamazaki |
| author_facet | Dongmin Gang Sungjoon Kim Kimyeong Lee Myungbo Shim Masahito Yamazaki |
| author_sort | Dongmin Gang |
| collection | DOAJ |
| description | Abstract We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[ T $$ \mathcal{T} $$ rank 0], to a (2+1)D interacting N $$ \mathcal{N} $$ = 4 superconformal field theory (SCFT) T $$ \mathcal{T} $$ rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = max α (− log| S 0 α + $$ {S}_{0\alpha}^{\left(+\right)} $$ |) = max α (− log| S 0 α − $$ {S}_{0\alpha}^{\left(-\right)} $$ |), where F is the round three-sphere free energy of T $$ \mathcal{T} $$ rank 0 and S 0 α ± $$ {S}_{0\alpha}^{\left(\pm \right)} $$ is the first column in the modular S-matrix of TFT±. From the dictionary, we derive the lower bound on F, F ≥ − log 5 − 5 10 $$ \left(\sqrt{\frac{5-\sqrt{5}}{10}}\right) $$ ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal N $$ \mathcal{N} $$ = 4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples. |
| first_indexed | 2024-12-17T22:37:25Z |
| format | Article |
| id | doaj.art-460bd7353665481eb0c29129bde3d5ce |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-17T22:37:25Z |
| publishDate | 2021-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-460bd7353665481eb0c29129bde3d5ce2022-12-21T21:30:03ZengSpringerOpenJournal of High Energy Physics1029-84792021-08-012021816510.1007/JHEP08(2021)158Non-unitary TQFTs from 3D N $$ \mathcal{N} $$ = 4 rank 0 SCFTsDongmin Gang0Sungjoon Kim1Kimyeong Lee2Myungbo Shim3Masahito Yamazaki4Department of Physics and Astronomy & Center for Theoretical Physics, Seoul National UniversityDepartment of Physics, Pohang University of Science and Technology (POSTECH)Korea Institute for Advanced StudyDepartment of Physics and Research Institute of Basic Science, Kyung Hee UniversityKavli Institute for the Physics and Mathematics of the Universe (WPI), University of TokyoAbstract We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[ T $$ \mathcal{T} $$ rank 0], to a (2+1)D interacting N $$ \mathcal{N} $$ = 4 superconformal field theory (SCFT) T $$ \mathcal{T} $$ rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = max α (− log| S 0 α + $$ {S}_{0\alpha}^{\left(+\right)} $$ |) = max α (− log| S 0 α − $$ {S}_{0\alpha}^{\left(-\right)} $$ |), where F is the round three-sphere free energy of T $$ \mathcal{T} $$ rank 0 and S 0 α ± $$ {S}_{0\alpha}^{\left(\pm \right)} $$ is the first column in the modular S-matrix of TFT±. From the dictionary, we derive the lower bound on F, F ≥ − log 5 − 5 10 $$ \left(\sqrt{\frac{5-\sqrt{5}}{10}}\right) $$ ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal N $$ \mathcal{N} $$ = 4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.https://doi.org/10.1007/JHEP08(2021)158Conformal Field TheorySupersymmetric Gauge TheorySupersymmetry and DualityTopological Field Theories |
| spellingShingle | Dongmin Gang Sungjoon Kim Kimyeong Lee Myungbo Shim Masahito Yamazaki Non-unitary TQFTs from 3D N $$ \mathcal{N} $$ = 4 rank 0 SCFTs Journal of High Energy Physics Conformal Field Theory Supersymmetric Gauge Theory Supersymmetry and Duality Topological Field Theories |
| title | Non-unitary TQFTs from 3D N $$ \mathcal{N} $$ = 4 rank 0 SCFTs |
| title_full | Non-unitary TQFTs from 3D N $$ \mathcal{N} $$ = 4 rank 0 SCFTs |
| title_fullStr | Non-unitary TQFTs from 3D N $$ \mathcal{N} $$ = 4 rank 0 SCFTs |
| title_full_unstemmed | Non-unitary TQFTs from 3D N $$ \mathcal{N} $$ = 4 rank 0 SCFTs |
| title_short | Non-unitary TQFTs from 3D N $$ \mathcal{N} $$ = 4 rank 0 SCFTs |
| title_sort | non unitary tqfts from 3d n mathcal n 4 rank 0 scfts |
| topic | Conformal Field Theory Supersymmetric Gauge Theory Supersymmetry and Duality Topological Field Theories |
| url | https://doi.org/10.1007/JHEP08(2021)158 |
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