Rigid models for 2-gerbes I: Chern-Simons geometry
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909770827431936 |
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| author | Roberts, David Michael Vozzo, Raymond F. |
| author_facet | Roberts, David Michael Vozzo, Raymond F. |
| contents | Motivated by the problem of constructing explicit geometric string structures, we give a rigid model for bundle 2-gerbes, and define connective structures thereon. This model is designed to make explicit calculations easier in applications to physics. To compare to the existing definition, we give a functorial construction of a bundle 2-gerbe as in the literature from our rigid model, including with connections. As an example we prove that the Chern--Simons bundle 2-gerbe from the literature, with its connective structure, can be rigidified -- it arises, up to isomorphism in the strongest possible sense, from a rigid bundle 2-gerbe with connective structure via this construction. Further, our rigid version of 2-gerbe trivialisation (with connections) gives rise to trivialisations (with connections) of bundle 2-gerbes in the usual sense, and as such can be used to describe geometric string structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05521 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rigid models for 2-gerbes I: Chern-Simons geometry Roberts, David Michael Vozzo, Raymond F. Differential Geometry Mathematical Physics Category Theory 53C08 (Primary), 57R19, 57R20, 81T99 Motivated by the problem of constructing explicit geometric string structures, we give a rigid model for bundle 2-gerbes, and define connective structures thereon. This model is designed to make explicit calculations easier in applications to physics. To compare to the existing definition, we give a functorial construction of a bundle 2-gerbe as in the literature from our rigid model, including with connections. As an example we prove that the Chern--Simons bundle 2-gerbe from the literature, with its connective structure, can be rigidified -- it arises, up to isomorphism in the strongest possible sense, from a rigid bundle 2-gerbe with connective structure via this construction. Further, our rigid version of 2-gerbe trivialisation (with connections) gives rise to trivialisations (with connections) of bundle 2-gerbes in the usual sense, and as such can be used to describe geometric string structures. |
| title | Rigid models for 2-gerbes I: Chern-Simons geometry |
| topic | Differential Geometry Mathematical Physics Category Theory 53C08 (Primary), 57R19, 57R20, 81T99 |
| url | https://arxiv.org/abs/2209.05521 |