Spin(7)-instantons on Joyce's first examples of compact Spin(7)-manifolds
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909846411935744 |
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| author | Galdeano, Mateo Platt, Daniel Tanaka, Yuuji Wang, Luya |
| author_facet | Galdeano, Mateo Platt, Daniel Tanaka, Yuuji Wang, Luya |
| contents | We construct $Spin(7)$-instantons on one of Joyce's compact $Spin(7)$-manifolds. The underlying compact $Spin(7)$-manifold given by Joyce is the same as in Lewis' construction of $Spin(7)$-instantons. However, our construction method and the resulting instantons are new. The compact $Spin(7)$-manifold is constructed by gluing a $Spin(7)$-orbifold and certain local model spaces around the orbifold singularities. We construct our instantons by gluing non-flat connections on the local model spaces to a flat connection on the $Spin(7)$-orbifold. We deliver more than $20,000$ new four-parameter families of examples of $Spin(7)$-instantons within the structure groups $SO(3), SO(4), SO(5), SO(7)$, and $SO(8)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03451 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spin(7)-instantons on Joyce's first examples of compact Spin(7)-manifolds Galdeano, Mateo Platt, Daniel Tanaka, Yuuji Wang, Luya Differential Geometry High Energy Physics - Theory 53C07, 53C25 We construct $Spin(7)$-instantons on one of Joyce's compact $Spin(7)$-manifolds. The underlying compact $Spin(7)$-manifold given by Joyce is the same as in Lewis' construction of $Spin(7)$-instantons. However, our construction method and the resulting instantons are new. The compact $Spin(7)$-manifold is constructed by gluing a $Spin(7)$-orbifold and certain local model spaces around the orbifold singularities. We construct our instantons by gluing non-flat connections on the local model spaces to a flat connection on the $Spin(7)$-orbifold. We deliver more than $20,000$ new four-parameter families of examples of $Spin(7)$-instantons within the structure groups $SO(3), SO(4), SO(5), SO(7)$, and $SO(8)$. |
| title | Spin(7)-instantons on Joyce's first examples of compact Spin(7)-manifolds |
| topic | Differential Geometry High Energy Physics - Theory 53C07, 53C25 |
| url | https://arxiv.org/abs/2310.03451 |