On the 576-fold periodicity of the spectrum SQFT: The proof of the lower bound via the Anderson duality pairing
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866917635133800448 |
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| author | Johnson-Freyd, Theo Yamashita, Mayuko |
| author_facet | Johnson-Freyd, Theo Yamashita, Mayuko |
| contents | We are aimed at giving a differential geometric, and accordingly physical, explanation of the 576-periodicity of TMF. In this paper, we settle the problem of giving the lower bound 576. We formulate the problem as follows: we assume a spectrum $\mathrm{SQFT}$ with some conditions, suggest from physical considerations about the classifying spectrum for two-dimensional $\mathcal{N}=(0,1)$-supersymmetric quantum field theories, and show that the periodicity of $\mathrm{SQFT}$ is no less than 576. The main tool for the proof is the analogue of the Anderson duality pairing introduced by the second-named author and Tachikawa. We do not rely on the Segal-Stolz-Teichner conjecture, so in particular we do not use any comparison map with TMF. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06333 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the 576-fold periodicity of the spectrum SQFT: The proof of the lower bound via the Anderson duality pairing Johnson-Freyd, Theo Yamashita, Mayuko Algebraic Topology High Energy Physics - Theory We are aimed at giving a differential geometric, and accordingly physical, explanation of the 576-periodicity of TMF. In this paper, we settle the problem of giving the lower bound 576. We formulate the problem as follows: we assume a spectrum $\mathrm{SQFT}$ with some conditions, suggest from physical considerations about the classifying spectrum for two-dimensional $\mathcal{N}=(0,1)$-supersymmetric quantum field theories, and show that the periodicity of $\mathrm{SQFT}$ is no less than 576. The main tool for the proof is the analogue of the Anderson duality pairing introduced by the second-named author and Tachikawa. We do not rely on the Segal-Stolz-Teichner conjecture, so in particular we do not use any comparison map with TMF. |
| title | On the 576-fold periodicity of the spectrum SQFT: The proof of the lower bound via the Anderson duality pairing |
| topic | Algebraic Topology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.06333 |