Dimension Reduction of Generalized ASD Instantons
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909466088177664 |
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| author | Galt, Dylan Ma, Langte |
| author_facet | Galt, Dylan Ma, Langte |
| contents | We study generalized anti-self-dual instantons defined over Riemannian manifolds equipped with a parallel codimension-$4$ differential form. In particular, for product Riemannian manifolds possessing such a form, we study dimension reduction phenomena, finding a topological criterion for bundles which, when satisfied, allows for a complete characterization of dimension reduction for the corresponding moduli space of generalized ASD instantons. By establishing an integrability result for families of connections, we then deduce explicit descriptions for these moduli spaces, including those of Hermitian Yang--Mills connections, $G_2$-, and $\Spin(7)$-instantons. When one factor in the product is a $4$-manifold, we establish well-behaved compactifications for these moduli spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17086 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dimension Reduction of Generalized ASD Instantons Galt, Dylan Ma, Langte Differential Geometry Mathematical Physics We study generalized anti-self-dual instantons defined over Riemannian manifolds equipped with a parallel codimension-$4$ differential form. In particular, for product Riemannian manifolds possessing such a form, we study dimension reduction phenomena, finding a topological criterion for bundles which, when satisfied, allows for a complete characterization of dimension reduction for the corresponding moduli space of generalized ASD instantons. By establishing an integrability result for families of connections, we then deduce explicit descriptions for these moduli spaces, including those of Hermitian Yang--Mills connections, $G_2$-, and $\Spin(7)$-instantons. When one factor in the product is a $4$-manifold, we establish well-behaved compactifications for these moduli spaces. |
| title | Dimension Reduction of Generalized ASD Instantons |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2405.17086 |