Explicit Non-Abelian Gerbes with Connections
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909994728816640 |
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| author | Rist, Dominik Saemann, Christian Wolf, Martin |
| author_facet | Rist, Dominik Saemann, Christian Wolf, Martin |
| contents | We define the notion of adjustment for strict Lie 2-groups and provide the complete cocycle description for non-Abelian gerbes with connections whose structure 2-group is an adjusted 2-group. Most importantly, we depart from the common fake-flat connections and employ adjusted connections. This is an important generalisation that is needed for physical applications especially in the context of supergravity. We give a number of explicit examples; in particular, we lift the spin structure on $S^4$, corresponding to an instanton-anti-instanton pair, to a string structure, a 2-group bundle with connection. We also outline how categorified forms of Bogomolny monopoles known as self-dual strings can be obtained via a Penrose-Ward transform of string bundles over twistor space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_00092 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Explicit Non-Abelian Gerbes with Connections Rist, Dominik Saemann, Christian Wolf, Martin High Energy Physics - Theory Mathematical Physics Differential Geometry We define the notion of adjustment for strict Lie 2-groups and provide the complete cocycle description for non-Abelian gerbes with connections whose structure 2-group is an adjusted 2-group. Most importantly, we depart from the common fake-flat connections and employ adjusted connections. This is an important generalisation that is needed for physical applications especially in the context of supergravity. We give a number of explicit examples; in particular, we lift the spin structure on $S^4$, corresponding to an instanton-anti-instanton pair, to a string structure, a 2-group bundle with connection. We also outline how categorified forms of Bogomolny monopoles known as self-dual strings can be obtained via a Penrose-Ward transform of string bundles over twistor space. |
| title | Explicit Non-Abelian Gerbes with Connections |
| topic | High Energy Physics - Theory Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2203.00092 |