Differential Models for the Anderson Dual to Twisted $\mathrm{Spin}^c$-Bordism and a Twisted Anomaly Map
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917531953922048 |
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| author | Han, Fei Li, Yuanchu |
| author_facet | Han, Fei Li, Yuanchu |
| contents | We construct differential models for degree-3 twisted $\mathrm{Spin}^c$-bordism and for its Anderson dual. The model for the differential Anderson dual is based on the framework of Yamashita--Yonekura. Using these differential models, we define a twisted anomaly map from differential twisted $K$-theory with inverse twist to the differential Anderson dual of twisted $\mathrm{Spin}^c$-bordism. The construction is described geometrically in terms of bundle gerbes, gerbe modules, and reduced eta-invariants of Dirac operators associated to the twisted data. Conceptually, this map is expected to be related to the anomalies of twisted $1|1$-dimensional supersymmetric field theories, in line with the perspectives of Stolz--Teichner and Freed--Hopkins. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Differential Models for the Anderson Dual to Twisted $\mathrm{Spin}^c$-Bordism and a Twisted Anomaly Map Han, Fei Li, Yuanchu Algebraic Topology High Energy Physics - Theory Mathematical Physics Differential Geometry We construct differential models for degree-3 twisted $\mathrm{Spin}^c$-bordism and for its Anderson dual. The model for the differential Anderson dual is based on the framework of Yamashita--Yonekura. Using these differential models, we define a twisted anomaly map from differential twisted $K$-theory with inverse twist to the differential Anderson dual of twisted $\mathrm{Spin}^c$-bordism. The construction is described geometrically in terms of bundle gerbes, gerbe modules, and reduced eta-invariants of Dirac operators associated to the twisted data. Conceptually, this map is expected to be related to the anomalies of twisted $1|1$-dimensional supersymmetric field theories, in line with the perspectives of Stolz--Teichner and Freed--Hopkins. |
| title | Differential Models for the Anderson Dual to Twisted $\mathrm{Spin}^c$-Bordism and a Twisted Anomaly Map |
| topic | Algebraic Topology High Energy Physics - Theory Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2510.27286 |