Adjusted Connections I: Differential Cocycles for Principal Groupoid Bundles with Connection
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910996887502848 |
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| author | Fischer, Simon-Raphael Farahani, Mehran Jalali Kim, Hyungrok Saemann, Christian |
| author_facet | Fischer, Simon-Raphael Farahani, Mehran Jalali Kim, Hyungrok Saemann, Christian |
| contents | We develop a new perspective on principal bundles with connection as morphisms from the tangent bundle of the underlying manifold to a classifying dg-Lie groupoid. This groupoid can be identified with a lift of the inner homomorphisms groupoid arising in Ševera's differentiation procedure of Lie quasi-groupoids. Our new perspective readily extends to principal groupoid bundles, but requires an adjustment, an additional datum familiar from higher gauge theory. We show that for Lie groupoids, the additional adjustment data amounts to a Cartan connection. The resulting adjusted connections naturally provide a global formulation of the kinematical data of curved Yang-Mills-Higgs theories as described by Kotov-Strobl (arXiv:1510.07654) and Fischer (arXiv:2104.02175). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_16755 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adjusted Connections I: Differential Cocycles for Principal Groupoid Bundles with Connection Fischer, Simon-Raphael Farahani, Mehran Jalali Kim, Hyungrok Saemann, Christian Differential Geometry High Energy Physics - Theory Mathematical Physics We develop a new perspective on principal bundles with connection as morphisms from the tangent bundle of the underlying manifold to a classifying dg-Lie groupoid. This groupoid can be identified with a lift of the inner homomorphisms groupoid arising in Ševera's differentiation procedure of Lie quasi-groupoids. Our new perspective readily extends to principal groupoid bundles, but requires an adjustment, an additional datum familiar from higher gauge theory. We show that for Lie groupoids, the additional adjustment data amounts to a Cartan connection. The resulting adjusted connections naturally provide a global formulation of the kinematical data of curved Yang-Mills-Higgs theories as described by Kotov-Strobl (arXiv:1510.07654) and Fischer (arXiv:2104.02175). |
| title | Adjusted Connections I: Differential Cocycles for Principal Groupoid Bundles with Connection |
| topic | Differential Geometry High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2406.16755 |