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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2501.00460 |
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| _version_ | 1866916547031728128 |
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| author | Jiang, Hongliang |
| author_facet | Jiang, Hongliang |
| contents | We establish a connection between three-dimensional self-mirror symmetric $\mathcal N=4$ superconformal field theories (SCFTs) and time-reversal invariant topological quantum field theories (TQFTs) arising from universal mass deformations. Focusing on the Abelian case, the ultraviolet (UV) SCFT is characterized by the charge matrix $Q$, while the infrared (IR) TQFT corresponds to an Abelian Chern-Simons theory with level matrix $K=QQ ^T$. We derive constraints on the charge matrix for self-mirror symmetric SCFTs and demonstrate that the Coulomb and Higgs branch Hilbert series of these theories coincide. Additionally, we derive a general formula for the superconformal indices of Abelian $\mathcal N=4$ SCFTs with arbitrary charge matrices. For SCFT with the constrained charge matrix, the superconformal index is argued to exhibit invariance under the inversion of fugacity associated with R-symmetry, providing further evidence of self-mirror symmetry. We explore various properties of time-reversal invariant Abelian Chern-Simons theories in detail and establish their connections to self-mirror symmetry in SCFTs from multiple perspectives. In particular, we introduce a quantity, dubbed Gauss generating function, which is real and thus invariant under complex conjugation for time-reversal symmetric TQFTs, in parallel with the superconformal index, which is invariant under the inversion of R-symmetry fugacity for self-mirror symmetric SCFTs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Time-reversal invariant TQFTs from self-mirror symmetric SCFTs Jiang, Hongliang High Energy Physics - Theory We establish a connection between three-dimensional self-mirror symmetric $\mathcal N=4$ superconformal field theories (SCFTs) and time-reversal invariant topological quantum field theories (TQFTs) arising from universal mass deformations. Focusing on the Abelian case, the ultraviolet (UV) SCFT is characterized by the charge matrix $Q$, while the infrared (IR) TQFT corresponds to an Abelian Chern-Simons theory with level matrix $K=QQ ^T$. We derive constraints on the charge matrix for self-mirror symmetric SCFTs and demonstrate that the Coulomb and Higgs branch Hilbert series of these theories coincide. Additionally, we derive a general formula for the superconformal indices of Abelian $\mathcal N=4$ SCFTs with arbitrary charge matrices. For SCFT with the constrained charge matrix, the superconformal index is argued to exhibit invariance under the inversion of fugacity associated with R-symmetry, providing further evidence of self-mirror symmetry. We explore various properties of time-reversal invariant Abelian Chern-Simons theories in detail and establish their connections to self-mirror symmetry in SCFTs from multiple perspectives. In particular, we introduce a quantity, dubbed Gauss generating function, which is real and thus invariant under complex conjugation for time-reversal symmetric TQFTs, in parallel with the superconformal index, which is invariant under the inversion of R-symmetry fugacity for self-mirror symmetric SCFTs. |
| title | Time-reversal invariant TQFTs from self-mirror symmetric SCFTs |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2501.00460 |