Deformed $G_2$-instantons on $\mathbb{R}^4 \times S^3$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866908391894417408 |
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| author | Fowdar, Udhav |
| author_facet | Fowdar, Udhav |
| contents | We construct explicit examples of deformed $G_2$-instantons, also called Donaldson-Thomas connections, on $\mathbb{R}^4 \times S^3$ endowed with the torsion free $G_2$-structure found by Brandhuber et al. and on $\mathbb{R}^+\times S^3 \times S^3$ endowed with the Bryant-Salamon conical $G_2$-structure. These are the first such non-trivial examples on a $G_2$ manifold. As a by-product of our investigation we also find an associative foliation of $\mathbb{R}^4\times S^3$ by $\mathbb{R}^2 \times S^1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_10380 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Deformed $G_2$-instantons on $\mathbb{R}^4 \times S^3$ Fowdar, Udhav Differential Geometry 53C07, 53C29 We construct explicit examples of deformed $G_2$-instantons, also called Donaldson-Thomas connections, on $\mathbb{R}^4 \times S^3$ endowed with the torsion free $G_2$-structure found by Brandhuber et al. and on $\mathbb{R}^+\times S^3 \times S^3$ endowed with the Bryant-Salamon conical $G_2$-structure. These are the first such non-trivial examples on a $G_2$ manifold. As a by-product of our investigation we also find an associative foliation of $\mathbb{R}^4\times S^3$ by $\mathbb{R}^2 \times S^1$. |
| title | Deformed $G_2$-instantons on $\mathbb{R}^4 \times S^3$ |
| topic | Differential Geometry 53C07, 53C29 |
| url | https://arxiv.org/abs/2208.10380 |