Deformation Theory of Asymptotically Conical Spin(7)-Instantons
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913585618223104 |
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| author | Ghosh, Tathagata |
| author_facet | Ghosh, Tathagata |
| contents | We develop the deformation theory of instantons on asymptotically conical $Spin(7)$-manifolds where the instanton is asymptotic to a fixed nearly $G_2$-instanton at infinity. By relating the deformation complex with spinors, we identify the space of infinitesimal deformations with the kernel of the twisted negative Dirac operator on the asymptotically conical $Spin(7)$-manifold.
Finally we apply this theory to describe the deformations of Fairlie-Nuyts-Fubini-Nicolai (FNFN) $Spin(7)$-instantons on $\mathbb{R}^8$, where $\mathbb{R}^8$ is considered to be an asymptotically conical $Spin(7)$-manifold asymptotic to the cone over $S^7$. We calculate the virtual dimension of the moduli space using Atiyah-Patodi-Singer index theorem and the spectrum of the twisted Dirac operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03646 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deformation Theory of Asymptotically Conical Spin(7)-Instantons Ghosh, Tathagata Differential Geometry High Energy Physics - Theory Mathematical Physics 53C07 We develop the deformation theory of instantons on asymptotically conical $Spin(7)$-manifolds where the instanton is asymptotic to a fixed nearly $G_2$-instanton at infinity. By relating the deformation complex with spinors, we identify the space of infinitesimal deformations with the kernel of the twisted negative Dirac operator on the asymptotically conical $Spin(7)$-manifold. Finally we apply this theory to describe the deformations of Fairlie-Nuyts-Fubini-Nicolai (FNFN) $Spin(7)$-instantons on $\mathbb{R}^8$, where $\mathbb{R}^8$ is considered to be an asymptotically conical $Spin(7)$-manifold asymptotic to the cone over $S^7$. We calculate the virtual dimension of the moduli space using Atiyah-Patodi-Singer index theorem and the spectrum of the twisted Dirac operator. |
| title | Deformation Theory of Asymptotically Conical Spin(7)-Instantons |
| topic | Differential Geometry High Energy Physics - Theory Mathematical Physics 53C07 |
| url | https://arxiv.org/abs/2305.03646 |