Parallel torsion and $G_2, Spin(7)$ instantons
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914179293642752 |
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| author | Ivanov, Stefan Petkov, Alexander Ugarte, Luis |
| author_facet | Ivanov, Stefan Petkov, Alexander Ugarte, Luis |
| contents | Instanton properties of the characteristic connection $\nabla$ on an integrable $G_2$ manifold as well as instanton condition of the torsion connection $\nabla$ on a $Spin(7)$ manifold are investigated. It is shown that for an integrable $G_2$ manifold with $\nabla$-parallel Lee form the curvature of the characteristic connection is a $G_2$ instanton exactly when the torsion 3-form is $\nabla$-parallel. It is observed that on a compact $Spin(7)$ manifold with $\nabla$ closed torsion 3-form the torsion connection is a $Spin(7)$ instanton if and only if the torsion 3-form is parallel with respect to the torsion connection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parallel torsion and $G_2, Spin(7)$ instantons Ivanov, Stefan Petkov, Alexander Ugarte, Luis Differential Geometry High Energy Physics - Theory Instanton properties of the characteristic connection $\nabla$ on an integrable $G_2$ manifold as well as instanton condition of the torsion connection $\nabla$ on a $Spin(7)$ manifold are investigated. It is shown that for an integrable $G_2$ manifold with $\nabla$-parallel Lee form the curvature of the characteristic connection is a $G_2$ instanton exactly when the torsion 3-form is $\nabla$-parallel. It is observed that on a compact $Spin(7)$ manifold with $\nabla$ closed torsion 3-form the torsion connection is a $Spin(7)$ instanton if and only if the torsion 3-form is parallel with respect to the torsion connection. |
| title | Parallel torsion and $G_2, Spin(7)$ instantons |
| topic | Differential Geometry High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.10623 |